My intuition is that people get confused whether they're measuring the risk to themselves or the risk to society from their Covid decisions.
It might be that public pressure focusing on the risk to each of us is obscuring some of the risk to other people, or it might just be a collective action problem - if a mayor encourages other people to be vigilant about Covid from his beach vacation in Mexico, well, that does much less damage as long as everybody else follows his advice.
Sorry for the late reply. I'm assuming you need to be "infected" in order to infect someone else (define "infected" so that this is true). Since being infected is a neccessary precondition to infecting someone else,
P(you infect someone else) <= P(you are infected),
and it's clear you can replace "<=" by "<".
This is basic probaility theory, I can't follow your notation but suspect that you are using some different definition of "infected" and/or confusing probabilities with expected values..
I recently realized a very simple, almost obvious bias, that I had because I never thought more about it. Moreover, quite a lot of people have this bias too.
What is worse in time of pandemic - to increase the number of your contacts from 0 to 1 or from 99 to 100? Intuitively, since we perceive many quantities on a logarithmic scale, the first thing is much worse. I heard multiple times something like: "I am already doing this and this and that because I have to, so it does not make sense for me to decrease my shopping", or "My roommate (spouse, child...) does not care about this at all, so it does not make sense for me either".
However, this is simply not true. If I care solely about myself, increasing the number of contacts increases the probability to get sick linearly - no logarithmic scale. But if I also care about other people (my contacts, yes), then we have linear growth of probability to become a spreader, and linear growth of the group to whom I can spread, thus leading to quadratic growth of the total expected damage to society.
So, if I have quite a lot of contacts already, I should be much more cautious about adding more than if I have almost none. It sounds so trivial right now - yet so many times I have heard the opposite advice.