Since my confreres have made such good sense on the why, how and what-for of push hands, I'll just put in my two cents on a more personal level.
In my group of Tai Chi brothers and sisters we have the penultimate pacifist sister. She is training TCC not for its martial context but strictly for its health side, period.
This fine lady resisted doing push hands for quite a while, because she felt it was a bit too "martial" for her tastes.
Well, one day she showed up a bit early for the form class and observed the rest of us having the time of our lives doing push hands.
After watching how entirely innocuous push hands is she has since begun training and is now one of the most avid practicioners of the art we have in our group.
Push hands is quite simply a lot of fun. It can also be frustrating when you're having a "not in the zone" day, but for the most part it's almost more fun than human beings should be allowed to have.
Rather than thinking of it as a "path to the martial art", think of it as a path to learning more about yourself and the art of TCC than any amount of form training can give you.
Believe me when I tell you, my Tai Chi sister would not touch the practice of push hands if she felt she was in any way being "martial" when she did so.
You learn about circling, weight distributions, moving energy and chi from push hands. You learn about yourself, you learn about others. You learn what works well for your body, you learn what doesn't work at all.
What you won't learn is how to be the next Bruce Lee. By itself pushing hands will not teach you the "martial art". That comes later, during sparring.
Push hands alone is not a "fight". It is a contest in which both players do nothing but win.
I tell people that don't want to train the "martial art" aspects of TCC that push hands is no more martial than a game of basketball or twister. You use your body to play those games, right? Same thing.
Well, actually since in push hands both players always win, it's even less competitive than that.
Further, this same wonderful lady now trains sword form with us as well.
We simply talk of the forms in terms of "energy and body movement" instead of "martial applications" when she is at class.
She enjoys learning the different ways you have to move your body in weapons training, because it carries directly back over into her tennis playing. For that reason, she is learning how to handle an object, move her energy into it and use it along with her body seamlessly to achieve a goal.
She says her tennis game has improved immensly.
Of course, the running joke now is that we're going to have to pick her up a "Stone Cold Killer" T-shirt to wear to class!
But that's just because we love to tease her. In reality, we all think it's wonderful that she's opening her horizons and learning more about this wonderful art.
That she is able to take the skills she is learning by doing so back into other "non martial" aspects of her life is a testament to how all encompassing the art of TCC can be.
Not everyone wants to become the next Yang Lu Chan. TCC embraces the health and kenesiology of life just as well as it embraces the martial arts.
One aspect is not more "legitimate" than another. All are perfectly acceptable reasons to train.
There are as many reasons to train TCC as there are students training it. Yours does not have to be the same as anyone elses.
Take what you want from it, leave the rest, but don't mistake the entire art as a martial art.
It is a life art.