It is completely false that men don’t have to cover up in Islam. Men are required to cover from their naval to their knee, and if he shows other parts of his body that he knows will cause temptation and will open doors to other evils, he has to cover it up as well. Now one might ask, “But don’t women have to cover up more than men?” The answer is yes, they do. Allah ordained this to happen in His Infinite Wisdom and one may not know the reason why, but if one is being realistic, men are way more visual than women. A man gets a lot more stimulated from looking at a women than vice versa, and this is backed up by scientific evidence. If a woman looks at a man, she may definitely be stimulated, but not nearly as much as a man. Now combine this with men being generally stronger than women, this will lead to many horrible things happening, such as rape and kidnap. This is why in almost all liberal countries around the world where women display their bodies, rape, sexual harassment, and sexual trafficking are on the rise. This is not to say that it’s a women’s have fault if incidents like this happen; men who do these crimes are certainly committing a massive sin. That being said, it is a two way job and both parties need to work together to prevent this evil. Men definitely have to do their part as well, such as lowering their gaze, dressing modestly, etc.
To conclude, it should be noted that in Pre-Islamic Arabia, they used to bury their daughters alive, as having a daughter was seen as a disgrace. Women were treated as property with no rights at all. Even in the western world, women were deprived of many of their rights until recently, such as voting. Islam liberated the women, gave them honor, dignity, and their due rights. This is why, despite all of these outrageous, ongoing allegations against the way Islam treats women, most people who convert to Islam are in fact women!
And Allah knows best.