You implicitly assume that one man can only have a relationship with one woman at the same time (or vice versa). If you drop that assumption (because it's BS), your reasoning just collapses.
This argument is wrong. A "hot man" or "hot woman" can have many partners in a short period of time, sometimes at the same time. Less desired people, as you can see in this thread and pretty much everywhere this topic is discussed earnestly, can go a whole lifetime without even a single partner.
In my experience, women absolutely have an easier time getting partners, and there's no contradiction. It's just that a few men are taking all the girls - always been this way (notice how many places used to even enshrine that in law by allowing marriages between one man and multiple women - quite a few countries to this day) and probably will never change.
*women tending to date men older than them and vice versa does mean that in an increasing population there might be more women in a particular dating pool than men than one would otherwise expect, but there might be negative feedback in the form of more pressure for age-reverse relationships to take up the slack