I do wish people would stop putting pregnancy/childbirth in the same category as sterilisation surgeries, they are not comparable.
Women do not have babies as a favour to their partners, they have them because they want to, so they are not owed.
If you decide that you, as a woman, do not wish to bear any more children, by any man, then you need to look at your options. One of these options is to ask you DP to have a vasectomy. If he won't then that is not a viable option so you look what other choices are available.
Men are people, not just insemination machines. And whilst a man may be sure in his head he doesn't want to father any more children, there can be a huge psychological barrier in transferring that into a permanent state of affairs. Perhaps he's not as sure as you think.
Also vasectomies are not always without pain and complication. If it goes wrong then permanent damage can be done! This is of course a scary thought. Odds are that it will be fine but that's no comfort for the men who are the minority suffering unfixable nerve damage.
Any op, no matter what for, should be the choice of the patient as they are the ones going through it, and they should never be forced or resented no matter how minor it appears to be.
I suspect that your DH has no objection to being sterile, but it's not the end result that scares him, it's the procedure and the fear of pain or damage. They are valid concerns and should not be belittled.