Let’s get this out of the way first: In general, men suck. 
I’ve seen perfectly reasonable-sounding men suddenly turn into raging douchebags when their advances were turned down.
I don’t (just) mean "when they were dumped" here. I’ve had multiple women show me messages where after only two or three exchanges, the women politely said they weren’t interested, and the immediate response was "you’re a bitch"… or worse. And the odds that a male ex will assault the woman who broke up with him are downright depressing.
One completely understandable response to this abhorrent male behavior pattern is that women will often give a series of reasons why they do not want (or do not want to continue) a relationship.
That makes sense. If there’s an external reason – scheduling, distance, still recovering from a past relationship, whatever – then it can give the idea that if there’s anyone/anything to be mad at, it’s not the woman who doesn’t want a relationship. And too often, men are so pushy and insistent and entitled that they will not stop until a "reason" is given – for example, naming themselves the "property" of another man (e.g. "I have a boyfriend/husband"). 
But sometimes that can get exactly the opposite response than women want.
For example, I’m a problem-solver. If I’m told that someone simply isn’t into me – which has happened a fair bit over my lifetime – that can suck, but there’s nothing really to be done about that. It is not a solvable problem, it just is.
If, instead, what I hear is "We can’t date because of [insert an external reason here]," then that means the problem is just that external reason. For example, "my schedule is too busy to date" translates as "but if my schedule was less busy, we would be dating." That’s a logistics problem to solve.
That kind of problem solving is a great quality… if that’s really the reason.
But if that woman just doesn’t want to start – or wants to end – a relationship, then problem-solving is not the desired response. That problem-solving behavior might come across as annoying and pestering – or worse.
I know that I have screwed this up in exactly this way before I realized or figured out what was going on.
For me personally, yes, it’s a thing that I continue to address and work on in therapy.
For other men – I so strongly hope this isn’t just me! – who worry that they may accidentally do the same thing, a beta reader of this post had a great suggestion. "If the external problem seems difficult, but you have an idea of how to problem-solve it, throw it out there. But if that’s immediately followed by another external problem being brought up, that’s a flag that this is a problem that she does not want to solve, and it’s time to let it go." This is something men can do to fix this problem.
Given how awful men typically are toward women, I am not saying that women should be doing anything that feels unsafe to them. Every beta reader for this post told me they’d had experiences of men being awful when they were turned down.
So I offer this as a pragmatic suggestion :
If giving reasons why you’re not interested in a man is not having the effect you expect, it might be a misunderstanding rather than malice, and being blunt and honest may get your point across more effectively.
 IMHO, it’s the fault of the patriarchy, but let’s acknowledge that this is a redonkulous over-generalization I’m making. Further, because I’m talking about societal gender roles in our current culture, I’m using "men" and "women" to describe those roles. I’m curious how (or if) this plays out with trans or genderqueer folks, but since I don’t have any data, I’m not speculating and just limiting to talking about my own experience with these two roles.
 That this is true disgusts me, by the way. Women should not have to call themselves property to have their wishes respected. Period.
 Meaning this is not about protecting men’s feelings; this is about hopefully minimizing the conflict women have to endure.