I'm not sure how to take the gender roles comment, but I'm somewhat offended that it was even brought up TBH.
You never get what you want if you don't state it. I want you to be healthy is a perfectly valid concern. Using nicotine is not as healthy as not using it. Intentionally inhaling anything of any sort in and of itself is a concern. More worrisome than the nicotine is the long-term safety of propylene glycol and vegetable glycerin, but in most of our minds those risks are worth it when compared to an alternative of combustion (and rightly so). There is not enough info provided to damn their relationship is what I'm saying, and I think it's out of line for suggestions of "leave his sexist ..." to even be insinuated subtly.
The bottom line is that general perception towards e-cigarettes/vaporizers is negative, and it takes education to break that perception. If I was in his shoes and I hadn't heard anything about vaporizers other than what was on the news, I'd likely voice concern as well...but because I'm not a very trusting individual, especially when it comes to general opinion, I'd be doing research on it as well. That said, not everybody is the same, and if scientific data/studies is what will do the trick to open his mind to it that's perfectly fine.
Offer personal experiences with your vaporizer and liquids, offer links to scientific data as requested in the OP, but please don't try to damn a relationship based on a paragraph that doesn't even touch on whether he's being any more than concerned. Obviously if she posted that her boyfriend was going to leave her if she didn't quit, I'd have an entirely different opinion, but "I'd give this thing up for him if I have to..." doesn't say anything more to me than the OP assuming the worst, that he would leave her over something so petty, and when emotions are involved the irrational and rational tend to bleed a bit...especially when mixed up with a stressful situation such as quitting smoking.
Let's try and help this lady out without telling her to walk out please. I can't think of a better way to get her to go to the corner store for a pack of smokes.