“I feel like part of the group now.”一句中“like part”之间为什么没有加“a”

part of与a part of同义。
如: This book like (a) part of the broken cup.
This is only (a) part of it; where’s the rest?

但是，part of比a part of通常更为多用，而且a part of有“一小部分”的含义。
再如： Falling over is part of learning how to ski.
Only (a) part of his story is true.
There is but one china and Taiwan is part of chaia.

应该注意的是，在使用(a) part of …时，of之后的名词若是单数，通常谓语也就视为单数，同样，of之后的名词若是复数，通常谓语也视为复数。
如：This piece of glass seems to be (a) part of a lamp.
Part of the passengers were injured in the accident.

找我的语感来看，有“a”的话读起来很别扭的。理论不会。。。

因为有OF SO卟＋A

其实我个人感觉，两种讲法都可以，本来英文用法就是很灵活的，并不像国内教科书上那么权威。当然这只是我个人观点……

两种讲法都可以