What makes so many philosophers believe beauty is objective?
Some component of beauty is shared evolutionarily across the species.
We all like fifths, they are clean and comforting in their simplicity -- they are usually the first intervals children sing, even when not prompted. Among the modes of eight successive fifths we tend to agree the most compact one, the Lydian is the prettiest, but we get sick of it fast, like eating raw honey. And if we are listening very long, we would rather listen to the one a fifth up, the Ionian, which is why it is the traditional Major scale.
We generally all feel the pull from Major into Lydian, and then when we let ourselves fall into the Lydian we rush to get out of it and if we do that, then at some point later, we need a palate-cleansing lift into a mode that is less sweet and a fall out of that back where we came from. Rhythm and Blues works, using the shortest sequences of transitions that do that trick for us. And almost everyone can feel it.
But that does not make up a great deal of our taste in music. Those are basic things that pass below our radar. Most of our sense of the beauty of sound is not determined by things that we all share.
So I think this has to do with the phrasing of the survey and traditional definitions. I doubt very many philosophers would claim most judgments of beauty are largely objective. But they may lean toward objective aesthetics existing. The R&B formulas are real and they cross cultural barriers. Rock music put them in a blender and took over the world.
There are probably objective trends to some degree about most things in which we judge the beauty. Those are clearly not determining: a pretty big majority of any given person's ratings of a song cannot be based on shared criteria, you can tell by how much they vary. But the trends do exist. So, for clarity, you can choose to define those shared trends as 'beauty' and write the rest off as 'taste'.
Beauty is in the eye of the beholder
I'm prepared to say "beauty is objective!" but with one catch: beauty does not describe a quality of any thing but it describes a relationship between a person and a thing.
So I would say, "X is beautiful" is not objectively true. But... listen to this... "I would say X is beautiful" is objectively true!
Furthermore, if I would say that X is beautiful, then the beauty of X exists objectively.
But that objective thing, the beauty of X, exists contingently on me. This objective beauty of X would cease upon my death.
Let's take a few examples:
Clear, running water is beautiful to me. Probably, it's beautiful to many people. It's beautiful. But if the human race were to die off, then so would the beauty of clear, running water.
Stars are beautiful to me, and probably to others as well. But if we had two suns, or if the night sky was as bright as the sun because the stars were together all so bright, then that would be something different, and maybe not beautiful. I don't know.
Air on the G String by Bach is beautiful. The melody with its sustained first note, a III tone, carried through the first, second, third measures until finally breaking into a VI tone and on and on is a beautiful matter of contrast and tension, confusion and clarity, etc etc etc. But without me to hear the song, or somebody to play it, there is no such thing as "the beauty of Air on the G String".
Why do some people say that beauty is objective?
Because it is their subjective opinion that such is the case.
Why is their subjective opinion such? Well for that you need to go into the arguments that they are presenting. For example: Liebnitz.
As for the bigger question: is beauty actually objective or subjective?
Well... on that the jury is still out.
The major disagreement on beauty comes from not a disagreement on beauty but relative perception of such due to other factors. For example, when looking at a scenery, you may evoke certain memories which may lead you to classify something more beautiful than you would have if there were no memories attached to it. If you strip beauty of those definitions that encompass subjective perceptions arising from subject's own emotions, then beauty tends to looked at as objective rather than subjective.
It cannot be objective. It's not defined anywhere, it has no exact specs therefore you cannot make an universal rule for it.
It will always be subjective, no matter what some completed in polls or not.
Even in extreme situations (like mutilation) some may find that more attractive than the normal so beauty will always be subjective.
The fact that so more (even a majority) agree on something does not make it objective.