My question is, should i prevent google from indexing such pages and profiles?
No. Every page you have indexed is another way for people to find you in search. Being visible for long tail search phrases isn't a bad thing. Their volume can really add up.
Not to mention every page Google finds to your site is another page where it can count links for your pages. Internal linking is often overlooked and can have an impact on rankings. PageRank is passed and anchor text in these links can only help you.
Would that make the "other" keywords i want to index more relevant?
No. You don't rank well for those phrases because you aren't relevant enough for those terms. Just because you rank well for one term it doesn't preclude you from ranking well for another term. A page can rank well for "social dating" and "meet new people" at the same time.
So, if you're not ranking well for those broader and more popular phrases, it's because there is more competition and they are ahead of you in the SEO game. The more sites competing for a search term the more difficult it is going to be to rank well for it.
If you want to rank well for those terms you will need to make sure your pages are optimized and you need to acquire quality incoming links to your pages. Pages from related sites that rank well is ideal but any site related to yours is good to have.
If you want to make sure your site is properly optimized read up on SEO on this website. If you have any specific questions about SEO that hasn't been covered here yet definitely ask and we'll point you in the right direction.