I think @flo may be asking why assumptions made by one person would make an ass out of the other person.
And my answer to that is that people just couldn’t resist the apparent cleverness of the truism, and say it even though it doesn’t really make much sense.
Perhaps the idea is that an assumption can tend to make the other person seem like an ass and/or seem to behave like an ass in the mind of the person who made the assumption, when the consequences of their incorrect assumption has affects before the assuming person understands what’s going on.
e.g.
Babs: “I’ll be at the coffee shop at 6 as usual.”
Bob assumes this means she want to meet him there at 6am the next morning. When Bob shows up, he thinks Babs has stood him up, so she seems like an ass to Bob – Bob has made an ass out of Babs in his mind.
And/or when Bob confronts Babs about it, he’s being an ass, and Babs may respond like an ass out of upset.
Of course, like so many truisms, it itself is presumptive, sounds more clever and accurate than it is, and is not true all the time.