From a biological perspective, sex is something of a mystery. First of all, it's inefficient. If you want to reproduce sexually, the first thing you need to do is get two individuals, one of each sex, together in the same place. Then, they have to like each other, at least enough to procreate. And, for males, that's the end of the biological role. Sure, humans, and plenty of other species, use males to help protect the offspring, or provide food, or for myriad other reasons. But if those males weren't there using up resources, there could be more females, and potentially twice as many offspring around. More offspring means a greater chance of success for a species.
Which is where researchers have looked for the problems that might be associated with asexuality. By the way, for the purpose of this, I'm going to talk about asexuality in general terms, in fact there are two quite distinct forms, true asexuality, where reproduction is by either fission (like in bacteria) or parthenogensis (where females produce eggs that turn into fully functional organisms), or self-fertilization (where an animal produces both eggs and sperm and is able to fertilize their own gametes).
But back to the problems. The first one is the build up of potentially damaging mutations. This is sometimes referred to as Muller's Ratchet. Basically, the theory is that copying between generations isn't perfect. Each new generation will pick up a few mutations from its parent. That means as time passes, the number of mutations will increase. On its own, each mutation is not a particularly big problem, but if you collect enough, your health is going to suffer, and the species will become less viable. Remember also, that mutations are generally irreversible, so it's not like they are going to fix themselves from one generation to the next. The male then, the theory goes, helps get rid of these mutations by bringing in new genetic information that mixes with the mothers, and hopefully slows the mutation rate.
There's a second theoretical problem that relates to the enviroment. In this problem, you have a species that's wonderfully adapted to where it's living. But then something changes. It might be a new virus that the species hasn't seen before. Or the temperature might start to change. Whatever it is, if you don't have a gene that allows you to adapt, you're in trouble. Males in this case are often the source of the needed genes that either allow resistance or adaptation.
At least those are the theories. What Dr. Patrick Phillips and his team from the University of Oregon wanted to figure out was whether the theories were true or not. In an advanced online publication in Nature Magazine he took C. elegans and manipulated it to turn it into a self-fertilizing hermaphrodite. Sure enough over time, these worms built up mutations, showing the first theory has merit. Then, when challenging the hermaphrodites with a bacterial pathogen, again they were unable to resist infection and disease. In both experiments, controls with hermaphrodites that could outbreed with males did just fine, showing that males do prevent these problems.
So, men can take heart, biologically we do have a function. And of course beyond the basic genetic role, human males, and males of many other species have expanded their role to protection and sharing in the general raising of young. Which is good, we wouldn't want to end up like the Triplewart Seademon. Males of this species are simply a parasitic bag of sperm attached to their female...