It's not perfectly clear, but my best guess is that the instructor intends:
I love all logic, but I don’t love deductive reasoning.
to contain two incompossible premises.
meaning if "I love all logic" is true, it requires "I love deductive reasoning" to be true.
and conversely if "I don't love deductive reasoning", then "I love all logic is false".
Ergo, this argument can never have both of its premises true.
If the premises can never be true at the same time, then an argument is valid (at least on the definition of validity where an argument is valid if it can never have true premises and a false conclusion).
Where the argument suffers a bit is on clarity. There's three issues here.
First, if the proof is at the level of sentential logic, then it's not clear that the first and second premises are such that they cannot both be true. To understand their incompatibility we need to use "all" and other concepts you may not have learned. We can formalize the argument as :
- ∀x (Lx -> Vx) [for any x if x is a logic, then love x]
- La -> ~Va [a = "deductive reasoning, it's a logic but "you don't love it]
These could not both be true. Thus with reference to the definition of validity (impossible to have all true premises and a false conclusion), this argument is valid.
Second, the argument uses "I". This gets a bit dicey due to two issues:
- Pronouns are always a worry. (this article by David Kaplan looks rather thick on demonstratives but there are some issues with using pronouns)
- "X loves" - this is dicey because it complicates things. A common whipping boy for the 20th century logicians was to look at how one could (a) love Sartre's fiction and (b) hate Sartre's philosophy. And to ask if this is simultaneously possible. Here, similarly, "I" could be confused about the meaning of "logic" and/or "deductive reasoning" and thus believe to hold both claims.
Third, while it seems pretty obvious, it's not perfectly clear that the two premises are entangled. This seems to be what's tripping up a commentor on my answer -- they are pointing out something true: 1. P. 2. Q. Therefore, R is invalid, because R can be FALSE when both P and Q are TRUE. This example is, however, not that. Instead, the two premises are related such that we can't just view them as completely separate -- thus, the validity. But that should be made explicit.
Sometimes this sort of thing depends on knowledge beyond just the rules. For instance,
- The moon is a giant tomato.
- The moon is a big piece of yellow cheddar cheese.
- Therefore, I ate salad for breakfast.
When each premise is considered independently as P,Q, and R. This argument is invalid. But if we accept that "P" and "Q" here are related such that if P is true, then Q is not true and if Q is true, then P is not true, then the argument would be valid because the two variables are not independent.
The question on the third point is how far do we expect someone looking at an argument to be able to connect these things before we're just being absurd and our argument is actually invalid.