This is true for the first 2 months or so, especially if you have options, but if a woman of sufficient beauty puts in a sustained effort to win your heart, your heart will become attached to her eventually. It's not only a mental decision, it's a physical reaction of her holding her heart against yours and synchronizing. This is how every attachment starts. She convinces you she is a safe harbor but once you are attached (not a conscious decision but more like the frog boiling in the water slowly) you realize one day that you now need her or she can "break your heart" (connection).
We can have this effect on them as well, and remember: it takes them longer to fall. So we at least need to resist this process of losing control until she loses control also (easier said than done).
At some point, you want a girl who can make you fall for her. IMO, there is no greater feeling than holding someone you love who loves you back. But that can only come with the risk of losing her and feeling pain. Trust me, I've spent my time alone thinking I was perfectly happy as well but didn't know what I was missing.