Matt Alexander's Quick takes

That can't possibly be your true objection to this line of reasoning, as it doesn't make sense, so what do you really believe? Let me speculate...

Seriously though, the reasoning is perfectly valid. If it's true that spiders will reduce the net amount of bugs in your home, then not killing spiders is something you can do to reduce the bugs in your home with zero effort. And, if you were killing spiders before, this means you actually reduce your effort, so the amount of effort required is negative. 

Your reversal test is not apt. Buying spiders (or other predator bugs) and releasing them in your home is incredibly costly in terms of money, time, effort, and attention when compared to deciding not to do something you were previously doing that took effort. If deciding not to kill spiders is a -10 amount of effort, buying and releasing live spiders is like a +1000, plus it costs money. The correct comparison would be if there is another -10 effort thing you could do that would have comparable benefit. But there isn't. 

If you did want to go through the trouble of expending +1000 effort and all the time and money and mental energy required to release live bugs, then indeed it would be more rational to buy poison or traps or whatever, and I think that's exactly what most people would do — and actually do, when the amount of bugs in their home rises to a level where they feel it warrants a response. 

There's also an ecological problem with releasing more spiders (or other predator) bugs to catch prey bugs. You might think that the number of spiders in a home will naturally grow to the equilibrium, that is, spiders reproduce until the population of prey bugs is no longer large enough to support further population growth. On this assumption, buying spiders would be a waste, and would just lead to a bunch of dead spiders in your home — not something people want. (Conversely, if you notice a lot of spiders in your home, like an unusual, disconcerting amount, it's probably because of a termite infestation or some other problem where a large population of prey bugs has arisen without your knowledge.)

Moreover, even in cases where people make reasoning errors, it is often simply an accidental error, and not a subconsciously deliberate error designed to mask psychological discomfort or inner conflict. People make reasoning errors all the time, particularly when it's a topic they've barely ever thought about at all. It's unusual to spend much time thinking about bugs. 

I think it's a dangerous habit to tell yourself stories about other people's mental states that serve to reinforce your belief that you're not just right, you're so obviously right that nobody could sincerely disagree you, so all disagreement must be self-deception. I don't think this habit serves the goal of "rationality", and I think it's one of the many mistakes made by the so-called "rationalist" community — which, in my opinion, is more systemically irrational than the general population. (For instance, the rate of the formation of cults or groups similar to cults in relation to the rationalist community must be something like an order of magnitude if not two, three, or four higher than for the general population. Why would anyone rationally take advice on rational thinking from that community given that abysmal failure rate? Why take fire safety advice from the neighbourhood with houses all aflame?)

One of the most important and most difficult habits to cultivate in service to rational thinking is simply the habit of engaging with dissenting views and perspectives with curiosity and open-mindedness, cultivating an emotional state (and social relationships, and group norms) where it feels emotionally comfortable to change your mind about things. A lot of the "rationalist" thinking tips I see people link to seem oriented around the opposite of this: debating to "win", boosting your sense of your own cleverness, scorning others for not being as clever as you, etc. This leads to disasters, of which there have already been too many (including the cults).

But of course everything I just said is so obvious, deep down you must already believe it, so let me work out why you're pretending you don't believe it...

Alternatively, people find engaging with bugs "yucky" so they prefer having an excuse not to step on a spider :\

I think it serves 2 purposes:

1. Most people want to feel like they are good, kind. Preventing harm to something much smaller/weaker than themselves reinforces this. Even better if it requires very little effort.
2. Social signal. I personally immediately trust people more if they take their spiders outside rather than kill them. I think they're more likely to have good intentions in whatever else they do. I think many people feel the same way and are vaguely aware that carrying themselves like this sends a useful signal to others.