If you want to say that analytic philosophy is similar to pure math, fine.  If you want to say that it’s similar to physics or other areas of “hard science,” you’ve got a problem.

Because (even) in hard science, we don’t treat successful formalization as the one and only criterion of worth.  We learn to make semi-intuitive, predictive judgments of whether an idea “looks like it’s going in the right direction,” even if it hasn’t been perfectly formalized yet.  We distinguish “there is an exception, and that makes your conjecture false in an important, devastating way” from “there is an exception, but it’s not one that matters for the sort of thing we’re trying to do, and I feel like the important content of your conjecture is true even if the formalism needs more work.”

“What you said isn’t technically true, but I know the sort of thing you are getting at, and it seems basically true and important to me” is the kind of thing we say all the time.  Even in the kinds of science where we use mathematical symbols and logic and things can be proven!

This isn’t just laziness; it’s an absolutely essential skill when you’re doing actual research, in which there are usually many possible roads you could go down, and you could spend weeks of your time on any them, if you wanted to explore them in full rigor.  You have to be able to distinguish “I haven’t done all the technical work here yet, but the core of the idea feels sound” from “there is a technical objection here that, unless I can figure out how to answer it, makes the idea unsound.”  If you can’t do this, you will waste a lot of time and you will not be a productive researcher.  In many cases, ideas that have of a lot of circumstantial evidence going for them end up getting used, in practice, for years or decades before anyone manages to prove that they in fact work.  People can tell that these ideas are “good” in a way that your typical just-plain-refuted idea is not “good.”

The kind of thinking that deems everything either refuted or not refuted, in which every technical objection has equal force and you can’t say you feel like an idea is going in the right direction unless you can answer every nitpicky objection to it – this is very alien to us in science.  People who act like this do not make good researchers.  They do sometimes make good mathematicians.  But if you want to compare your work to science rather than math, well, we don’t actually work that way.