The common name for the system in which men and women manipulate one another is called "patriarchy". (When you look beyond men and women, it's called "kyriarchy".) It's bullshit on both sides.
There are two reason it's seen as worse for men, both historical. One is the men have had way more power and are still substantially advantaged. The more power you have, the more responsible you are for a fucked-up situation.
The other is that people with less power are forced to be manipulative to survive. E.g., 100-200 years ago, when professional women were very rare, women focused a lot marrying well, because they didn't have a lot of other options. So there's a bunch of cultural hangover from that.