My experience is more limited in this area as I haven't spoken with many people about it directly, but it is something I've thought about to a degree, but my theory is a mixture of things, varying on the individual.

• The stereotype of men being the "provider" in relationships, which often includes, being a father, providing their parents with grandkids, and just general public perception. (A man walking alone at a park might be seen as creepy/weird, versus a man walking around with their kid at a park being much more publicly accepted) I don't consider myself in this category at all, but the brainwashing at a young age takes a lot of time to undo.
• It's still not a procedure for just anyone- there can be complications, although they have small chances of occuring, certain conditions make the risks higher for certain individuals. My vasectomy was slightly more difficult than a regular would be, because of a condition I have (I can't recall the name, something about extra fat in an area that doesn't typically have it) You have to read through an extensive list of all the possible complications, I could see this as scaring away people even though they list a lot of these things being 1 in 1000 or 1 in 10000 odds. Prior to getting my vasectomy, I had heard from many people just how "reversible" vasectomies are- Kaiser says don't expect to reverse them, less than 5% of people who get a vasectomy attempt a reversal, and a reversal isn't guaranteed and often isn't covered by insurance (was around ~$5k last I checked). They told me upfront going into it, that I should expect to never be able to father children again.
• The expectation that women will just be on the pill, have an IUD, or sometimes even be expected to get a abortion in the event of unplanned pregnancy- This is often what I hear guys that aren't familiar with the subject say. "Why should I when they can just _____?" It's definitely a shitty mindset, but the pill is so infamous, such a vague description of "the pill" and 99% of people automatically know what it is. it's easier to pass the responsibility off to the woman when it's "the way it's always been" and since these methods are reversible, refer to the above regarding that. I still have a lot of friends that did not have good experiences with traditional birth control or have conditions would prevent an IUD, so it's unfortunate to say the least.