If we are saved by Grace why do so many believers try to live by the law? That would mean you were trying to save yourself.
I suspect it is a misunderstanding of both the concepts of Law and Grace, but that would take quite a while to explain properly.
A shorter answer is that people find it much easier to follow prescriptive rules than to internalize deeper principles and then make their own decisions. Also, those rules bring extra things like group identity, the ability to feel superior, to exclude others, etc. The fact that Paul basically warns against this kind of thinking doesn't stop modern Christians from falling into it on a regular basis--even to the point of treating Paul's own teachings as if they constituted a set of behavioral laws that one must follow to the letter. So they've taken his admonition that all in Christ are free of Law, nodded sagely, and then proceeded to replace the old Law with a new one, as if it were somehow completely different this time around. You could power a major metropolis if you could somehow attach an electrical turbine to him, so rapidly and constantly must he be spinning in his grave.
(I jump directly to a Christian focus because, of course, this question is of uniquely Christian interest. I'm not sure there are any other traditions to which it would apply.)