I should probably start right out by warning you that this is going to be a rant, a diatribe, a polemic. This expression is one of my least favourite ever and, for too long, I've let my anger simmer. Now finally I'm going to try and collate all the different reasons why you should never ever say it and why, if someone should have the bad taste to say it to you, you should just walk away.
The first thing is that it reeks of anti-intellectualism. There is a sort of implicit assumption in the expression that too much thinking is bad for you. Lots of situations warrant deep complex and involved thought and, while naturally it's possible to overthink even these problems, I feel it should go without saying that it is far better to overthink than to underthink something*. In one situation you risk offending, upsetting or hurting someone, in the other you risk sitting and being in your own head for longer than necessary.
I think the anti-intellectual bent can be seen more clearly when you notice that there is no equivalent opposite expression. Naturally you could tell someone that they weren't thinking enough, but there is no single expression to that effect. This despite the fact that I think there are definitely situations where people underthink. In fact, I'm going to take a little time out to try and show that this skewed perspective is the cultural norm in our society.
So, by way of making that point, let's look at Hollywood. Obviously in some ways that is a lowest common denominator cultural example, but I think it shows the trend fairly well. It is depressingly common that the entire arc of a film follows a straight laced individual, who overthinks, as they are taught how to be more impulsive (often a man being shown by a, frankly insulting, ditzy carefree girl stereotype). Then obviously they can finally enjoy life (as though life, if any thought is involved, cannot possibly be enjoyed). Again we can see there is no equivalent opposite movie, no one ever learns that they should think about things before they do them. In fact there are even several examples about unthinking individuals who have hardships but, eventually, come out on top because deep down they're such good people and they're “acting from the heart” (unlike all the poor people around them disabled by thought). **
Sure, you could say I'm overreacting here. There is an argument that the reason for this disparity is that impulsive actions are fun to watch, that having the film this way around makes for good scenes where the hero finally lets themselves go (though honestly I think this is unimaginative). My personal interpretation is that Hollywood has simply learned that people love being told they should 'be themselves' (an almost equivalently meaningless piece of advice) and don't want to hear that they should try being smarter and more considered.
The final criticism I have is that this is awful awful advice. If someone is overthinking something (and god knows, I do accept that this can happen) then probably they know that, but even if they don't, it is still equivalent to telling a depressed person that they are 'getting too sad', that is, it describes the problem in a completely advice-less manner. This is particularly hateful when we realise that almost the only time this expression can be used is when someone is describing their thoughts about a problem. That is, specifically when they are looking for advice.
In the case when someone is actually overthinking something there is plenty that can be said of use, most of it along the lines of 'I think you should do this' or even 'you've thought enough about this, you should just act now'. The fact that this expression seems so ubiquitous and accepted is starting to feel more offensive to me the more I think about it.
I feel in summing up I should point out that this wasn't triggered by any particular incident. I have had this said to me, certainly, but not on any notable occasions in the past few months. Honestly I would really like to see the opposite expression coming into effect. After all a lot of the time, it is specifically through thinking about and running over my problems in my head that I start to find solutions and become happier about them. I may well start telling people that they're underthinking it, if only to see how they react.
*[That's right, I just made up the words 'overthink' and 'underthink', it was just too easy a possibility to ignore. Besides, I quite like them, they sound like the opposing sides in a bad 70s science fiction film]
**[I thought I should back up these tropes with some examples. The first type (overthinker learns to underthink) is really well defined here tvtropes (with a list of examples at the bottom, under 'films'). The second type (underthinker succeeds) can be seen in almost any comedy film with a stupid main character, but examples are: Our Idiot Brother, Forest Gump, Dumb and Dumber, and almost any film with Adam Sandler.]