@Madwelsh has been a bit vague as to his partners reasons for wanting him to have it, other than to say her implant is due to be out soon and that they have 2 children already. Her 'moaning' may not just be moaning for no reason, we've got very little to go on. That said, sterilisation for either partner should be thought long and hard about by both parties and should be a decision made together on equal terms. He shouldn't feel pushed into it, but then he isn't being honest about not wanting it which won't be helping.
With regard to reasons why women may want men to have it. Quite often (though not always) it's women who take on the responsibility of contraception when in a long term relationship. Many women don't have an easy relationship with contraception, experience various side effects (moods changes, erratic bleeding patterns, pain etc) and have changes to their body due to it. As women age some methods of contraception are no longer available and choice becomes more limited. Sterilisation is also an option for women, however, usually it requires a general anaesthetic rather than local. There is also a higher failure rate. If the procedure fails it may increase the risk of ectopic pregnancy. None of these are reasons why a man should have to have the snip if he doesn't want to. Just trying to give another perspective on why some women may not just be moaning and might have good reason if the husband doesn't have an objection.