I'm going to extrapolate more on this later, since my workday is just kicking off.
But my upbringing was a pretty traditional working class cultural Christian type upbringing, and most definitely I was discouraged in showing what would commonly be called feminine traits.
Crying was not really acceptable. Showing strong emotions was generally seen as weakness, etc.
In some ways that's what people might think of as 'toxic masculinity', but I don't really see it that way. I also don't see it as particularly healthy, but that will take some explaining, in terms of where the line is. So,
@JustGeorge , I don't think the OP is really suggesting 'Why do no straight men have feminine qualities'. Rather it's 'Why are certain traditionally feminine behaviours discouraged by some/many mainstream cultures in straight men'.
Just like there is diversity in culture, and in gay men and how they express, there is too in straight men.
Still, it's undeniable that some things are commonly thought of as feminine in some cultures (eg. crying) and some cultures discourage those expressions in straight men.