Making fun of things is actually really easy if you try even a little bit. Nearly anything can be made fun of, and in practice nearly anything is made fun of. This is concerning for several reasons.
First, if you are trying to do something, whether or not people are making fun of it is not necessarily a good signal as to whether or not it's actually good. A lot of good things get made fun of. A lot of bad things get made fun of. Thus, whether or not something gets made fun of is not necessarily a good indicator of whether or not it's actually good.[1] Optimally, only bad things would get made fun of, making it easy to determine what is good and bad - but this doesn't appear to be the case.
Second, if you want to make something sound bad, it's really easy. If you don't believe this, just take a politician or organization that you like and search for some criticism of it. It should generally be trivial to find people that are making fun of it for reasons that would sound compelling to a casual observer - even if those reasons aren't actually good. But a casual observer doesn't know that and thus can easily be fooled.[2]
Further, the fact that it's easy to make fun of things makes it so that a clever person can find themselves unnecessarily contemptuous of anything and everything. This sort of premature cynicism tends to be a failure mode I've noticed in many otherwise very intelligent people. Finding faults with things is pretty trivial, but you can quickly go from "it's easy to find faults with everything" to "everything is bad." This tends to be an undesirable mode of thinking - even if true, it's not particularly helpful.
[1] Whether or not something gets made fun of by the right people is a better indicator. That said, if you know who the right people are you usually have access to much more reliable methods.
[2] If you're still not convinced, take a politician or organization that you do like and really truly try to write an argument against that politician or organization. Note that this might actually change your opinion, so be warned.
I think situation plays a role here as well though.
If I'm reading the comments section on Shakesville and see some rando come in with a basic question and get hit with the "I'm not your sherpa" card and a link to 101 materials, that's fine. You can't drop everything to debate every random dude who expresses a disagreement; I certainly don't appreciate it when people wander into the bio department and start up debates about irreducible complexity (yup, true story).
On the other hand, if I'm on GiantITP having a fun conversation about the best way to generate ability scores in Dungeons and Dragons (3d6 down the line, BTW) and someone goes full RadFem and derails the thread into talking about "biotruth" and privilege until it has to be locked, my jimmies get considerably rustled. Especially when I recognize a lot of the same rhetorical techniques I saw up in the first example.
That's the general point I was making; these tools are useful for defense, but unfortunately just as useful for offense.
In fact I suspect much of the feminists' need for defense comes from the highly aggressive ways they tend to go on offense.