I'm appalled by the fact that so many women seem to think that you are demasculating your man by asking a simple question, thereby insinuating you should keep your mouth shut!!
What I see here is that you offered a suggestion, followed up ONCE with a 'did you do it?' and then asked why not when he said no. Where's the badgering and nagging in that?
On a side note, maybe a less aggressive 'how come' instead of 'why not' (and tone of voice means everything in these situations) may have yeilded a different reaction.
You have every right to know why your premiums doubled and he (or you, in my house I would be doing the investigating) should find out, whether you stay with that company or not. What is he hiding by NOT asking? If it is a simple as nothing happened and it's a general increase in rates then by all means let him shop around.
Do NOT let him treat you that way over something so silly as asking him ONE TIME if he took your suggestion!!