I think you’ve mentioned two options and assumed all lead to the same results. So let us break them down.
1. Being armed increased the chance you’ll be harmed.
My read? Possible, even probable especially if you include suicide (which IMHO, should be legal and with little to no stigma attached to it, but that’s a whole other thread), the possibilities of accidental discharge and unauthorized users.
2. Learning self-defense increases the chance you’ll be harmed.
This one is tricky, because we’ve already had to try to define several different sorts of Self-Defense in a 20 post thread. Four general categories SO FAR, including Defensive Awareness, Self Defense Short Form (1-2 lessons or lectures), Martial Arts (presumably a few months to a few years), and Firearm/CCW training classes.
So now we’ve ballooned out to at least 6 different possible scenarios, all with potentially different answers. That’s why I tried to at least define the categories we have so we can discuss this in more detail. @Aspidistra did a very good job upthread of indicating, for women at least, that the first category, and possibly the second are beneficial to women at a minimum. I know people who seem to think not resisting an being raped is less ‘harm’ than fighting back, but I doubt anyone here is in that faction.
Martial Arts meanwhile, we’ve had a couple of perspectives - you know enough that you don’t know and trained reflexes that kick in without thought. I personally did Karate for about 4 months, enough to realize I didn’t have good muscle memory and stopped. I would say it didn’t embolden me in anyway, so lacking any statistics, we’re down to personal anecdotes.
Lastly, the Firearms/CCW training. @Gray_Ghost and I have already done this one to death in a prior thread, so I’ll just add my support that most professional trainers are dead set on talking you OUT of using your concealed firearm unless you are at personal risk of life. They know the legal, financial, and heck, even moral risks of using a firearm, and there is zero talk of shooting to ‘wound’ or ‘warn’. If you need to do either, you’re not a risk. So, no, the training probably doesn’t contribute to additional risk.
The group I would personally be most afraid of, is the armed group who has NOT had training, and are going to overreact in a threat situation. Right now, I see two main groups for this: Right leaning arsenal owners, who are looking for a TEOTWAWKI (the end of the world as we know it) as an excuse to be a hero by their own personal definition, and left learning first time gun owners who bought firearms ‘just in case’ due to COVID/Panic/Riots/Etc. Both groups have the weapons, but most likely do not have the training or the mindset to make an informed judgement in the heat of the moment.
Which brings me to my last point - I bet the answer varies HEAVILY depending on demographics. Education, location, economic group, sex, and of course, age probably figure largely into this. I mean, if you’re a teen/20 something male, you are already biologically primed for poor decision making, especially in a fight or flight situation. While if you are in the same group as a female, you’re a prime TARGET of violence, and your attitudes are likely less confrontational.
So TLDR - it’s too broad a generalization, and the answers are going to vary depending on a huge number of factors. 
Some food for thought -