You really do need to define what you mean by faith. People mean vastly different things when they talk about this topic all the time, and any refusal to pin down what they specifically mean is usually just an attempt at leaving wiggle room to avoid confronting hard truths or even move goal posts.
Here is my best take on your question from a couple of different definitions of faith. If your impression of what faith means is fuzzy rather than precise, you should still be able to extract a correspondingly fuzzy gist from the collective impression of each of these following responses. Naturally there will be some overlap in the meanings and responses. You also may agree with some definitions and disagree with others, or find only some apply to you personally. That is okay, but shows again why you should provide your own definition.
1. Faith as complete trust or confidence in someone or something
Why would this be a problem? Why would this be seen as a sign of weakness? Why might someone claiming this virtue be seen as 'inferior'?
Complete trust is not to be taken lightly. To whom can we give our complete trust? To whom or what would it be perhaps unwise (some would say stupid) to give our complete trust?
A Christian might put their complete trust in any number of things. The Bible? Their spiritual mentors? Their personal spiritual feelings/relationships? We can make fuzzy generalizations, but ultimately every individual Christian can decide for themselves which things or people to put in their 'complete trust bucket', and which things do not deserve that level of trust.
In this aspect of faith, someone may relate faith in X to weakness or inferiority if they disagree about giving complete trust to X.
2. Faith as unquestioning trust or confidence in someone
This is where a lot of people have sentiments that drive them to contrast faith with science.
This is also closely related (if not synonymous) with complete trust. Just emphasizing unquestioning here.
Science of course is known for being wrong. It makes no 'absolute conclusions' and holds no 'sacred truths'. Or barely any, if you want to nitpick the philosophical underpinnings. The physical theories themselves are not sacred. Every conclusion is a so-called 'tentative' conclusion, rather than absolute. Each conclusion has a level of precision presented up front - the margin of error. There are no sacred truths, only our best current models that indeed we hope to disprove someday.
In science, you are allowed to question every conclusion others have made up to this point. Nobody is forcing anyone to believe the speed of light is constant - you can go out and do the measurement yourself. You really can.
In this way, the scientific body of knowledge is imperfect, but pretty much trustless. At least when done thoroughly (especially regarding independent experiment reproduction).
Note that word - trustless.
This is in complete contrast with anything that asks for (or even demands) 'complete trust' or 'unquestioning belief'. It's like saying "take my word for it" for very bold claims.
What science tells us is that true propositions don't don't care whether you put your complete trust in them or not. True propositions don't need, and especially don't demand your unquestioning belief. Truth can stand on its own two feet. Take Proposal X. If it is true, what does it have to fear from questioning? Go ahead and question it, if you are seeking truth, you will arrive at the conclusion it is true. If X is false, then it DOES have to fear from questioning. If false proposals tend to be culled very easily by questioning, then the false proposals that survive will be the ones that implicate virtues of unquestioning belief.
In other words, unquestioning belief is only a virtue to the gullible, and only promoted by liars and scam artists with something to hide, or something to hide from.
If Alice sees Bob as gullible, that will scar Alice's impression of Bob's intelligence, and she will very likely lose a bit of respect for him.
3. Faith as loyalty in a relationship
Nothing wrong with this strictly speaking, except when taken to the extremes as in the above cases.
Faithfulness in a marriage is highly encourageable. Of course.
One might analogize to a relationship with God, so faithfulness is important there too. Sure.
But what happens if one of the spouses in a marriage turns extremely abusive, violent even? This is where the extremes of 'unquestioning loyalty' and uses of faith as a form of absolutism break down - are no longer admirable.
If a spouse becomes extremely abusive, maybe we should have some level of tolerance to work through problems, but there are definitely limits. Is it a relationship, or enslavement? The relationship has to cut off at some point. Loyalty isn't owed forever. In a similar vein, we can analogize to God again. If God or religion becomes abusive to your or your life, you don't owe them undying loyalty. You don't owe anyone undying loyalty. You're not a slave. You're a human being free change association with whoever or whatever you want, and put limits on your loyalty.
Along the lines of gullibility, unquestioning loyalty isn't admirable. It's sad.
However loyalty isn't bad in itself. This aspect of faith isn't bad strictly speaking. It is only bad when taken too far.
So someone might feel bad for you if they think your loyalty is being abused.
4. Faith as spiritual apprehension, spiritual perception
Perhaps some Christians feel personally touched by the God. This witness of the Holy Spirit is evidence of God to them.
Whether or not this constitutes 'valid evidence' for Christianity (or any religion with similar experiences) depends on your epistemology. This is one of those fronts where people argue past one another forever and ever because they never take the time to agree upon (or even find out) their premises. If two people don't narrow down where they agree and disagree with epistemology first, they will never be able to resolve a disagreement over 'evidence' of this nature, or indeed what constitutes 'valid evidence' in the first place.
Sadly, most debates or discussions where disagreement raises over validity of spiritual apprehension never settle the agreed epistemic foundations in advance. Most people just have their way own way of thinking, and that's just how it is. Then if Alice reveals reason X for belief Y, but X doesn't make any sense on top of the epistemic foundations Bob has, then Bob will think reason X is rather silly. Bob thinks Alice believes Y for very a nonsensical reason.
- Alice: "I only believe government sanctioned knowledge. What do you think of UFOs in area 51?"
- Bob: "I believe everything my favorite podcast host says. UFOs in area 51 are aliens"
- Alice: "Wow, that's a stupid belief for a stupid reason"
- Bob: "Keep drinking your koolaid"
- 5 year old: "Santa brought presents last night!"
- Uncle: "Oh? What makes you think it was Santa?"
- 5 year old: "uhh... It was what I was told. I was just raised this way. I believed it by default."
- Uncle: "Maybe we should consider whether things are true or not before accepting them. Have you considered what might make good criteria for accepting a proposition as true?"
- 5 year old: "whoa dude, slow down, I'm only 5"
- Parent: "ARE YOU GOING ON ABOUT YOUR STUPID EPISTEMOLOGY AGAIN? GET OUT OF HERE JUST LET THE KID ENJOY SANTA FOR CRYING OUT LOUD"
Fundamentally, some people don't put stock in spiritual apprehension. It can be really powerful because it is so personal, but unfortunately that can't really be made objective. It's a personal anecdote, not material evidence. Some people see spiritual perception and spiritual apprehension as nonsense, and not worthy of drawing conclusions from. They see this aspect of faith as magical thinking taken seriously, which may be seen as weak or inferior.
5. Faith as walking under the guidance of God
I looked up the famous 2 Corinthians verse about "Walking in faith and not by sight." Out of context you can apply any of the definitions. I tried to understand it in context though, and the above definition is the impression I get (sorry if it is incorrect despite my effort). It's also something I've heard my Christian friends relate before, so anyway.
Ultimately, if somebody doesn't believe in God, they have to look at the world with their own eyes, and have to take accountability for guiding their own life. In fact, to someone who doesn't believe in god, everyone needs to look at the world with their own eyes, and everyone needs to take accountability for guiding their own life.
Plato's cave is an interesting allegory, but by no means a useful argument. When two opposed perspectives clash, who is in the cave and who is enlightened? The allegory isn't an argument, it's just an analogy.
So maybe indeed it is the atheists or non-Christians who are enslaved to watch shadows.
BUT, that's obviously not how they see it.
Nobody confident in their beliefs sees themselves in the current moment as the slaves watching the shadows.
To someone who doesn't believe in god, saying "Walk by faith and not by sight" is exactly equivalent to saying "Walk with your eyes closed so that you're blind to what's around you" and consequentially the "Blind will lead the blind".
Sounds like a mess, right? You don't have to agree. It could a completely incorrect perspective to see faith as the guidance of God in that way. But regardless of the correctness, that is a perspective some people might have. And then having that perspective, that could contribute to why they look down upon faith in this regard.
Faith doesn't mean the same thing to everyone. This goes not only for the definitions, but the implications of the definitions, and then the value of those implications.
To many people, the unknown is a great opportunity and an unexplored land. However, an opportunity is not an opportunity if you decide outright you will never take it. An unexplored land is worthless if it is never on your agenda to explore it. While not everyone agrees on what faith is, to a lot of people, faith implicates closing your eyes, shutting your ears, clinging to the known, and letting others decide your life. To these people, faith is the opposite of an opportunity and spirit of exploration.
People with this perception of faith will naturally see faith as a sign of weakness (or inferiority if they have an arrogant streak) when another person espouses faith with pride.