"Stop analyzing a woman's actions" - Do you really mean that? That seems like either a poor choice of words or just terrible advice.
Also, "Men have to stop analyzing women's action and words." - I only half agree with you...women's words are meaningless.
Here's the deal....women value their sexual value above all else. It is driving factor with them. Look at the grocery store aisle with all the gossip magazines. Gossip magazines are a ranking model system using hollywood's finest in order to constantly assess celebrities' value on the market. Women use that model as a sort of gauge to help them value the men around them, other women around them (i.e., the competition), and themselves. A huge amount of computational time is spent in a woman's brain assessing the value of herself and everyone around her because one's value can change on a dime.
So, you can see, a woman's value is top priority. Now, lets get to the actual behavior...."Nice" girls say "nice" things. Generally, a women will never intentionally say anything bad about herself. Her words are constantly full of white lies, even your own mother does this. They do it without thinking. It's a subconscious, evolutionary thing.
Therefore, the only way to truly understand what a woman is plotting is by her ACTIONS. The greater the series of actions you can observe from her, the better understanding you get on what's really going on in her brain.
ALWAYS translate a woman's words through her actions. Constantly translate, otherwise, you are in for a world of hurt. Translate even what your own mother tells you.
I agree that you should not care with what a woman thinks of you, but you should pay attention to all women's actions, even the one's you are not interested in because it will help you understand them all and make you more successful with women.
Also, a lot of times women are questioning you, or seem to be judging you, or starting an argument....they are sh*t testing you to assess your value for a relationship. So, you do need to be concerned with this, because if you pass her tests, she is yours, at least for a while, anyway. But, deciphering a sh*t test is tricky and takes experience. Some women are so insecure that have the most bizarre sh*t tests, like insulting you, putting you down. How you handle that determines what happens next. Some women have fairly normal sh*t tests. The ones that have crazy sh*t tests, tend not to get into few LTR in their lifetime.
When they say a couple "clicks", in many ways, what that means is the man is really good at disarming a woman from her tests and makes her feel, safe and secure, and therefore she can give her heart to you. What you decided what to do once you get to that point, is up to you.