The authors modeled a 3d penis and vagina and showed that the penis is able to scoop out paste from the vagina. They then interpret it as that it’s “possible” for the penis to have evolved the way it has to scoop out rivals’ semen.

The obvious counter to the claim is that anything can be used as a shitty scooping spoon if you try hard enough.

The starting point is the focus on ways in which human sexual behavior is different from those of our closest living relatives, other primates and apes, and how the observed sexual behavior of those other species correspond with physical characteristics in their genitals.

I found this paper to be pretty interesting, and it has a decent summary of why the semen pumping theory sticks around despite some pretty significant issues. It proposes its own theory for the glans penis, but the discussion of the history of the displacement theory is good background on its own.

Basically, species with low sperm competition (where each female tends to mate with only one male) have smaller testes and smaller sperm midpieces (the motor unit that actually drives movement), and species with high promiscuity and high sperm competition, like chimpanzees, tend to have larger testes and larger sperm midpieces. And on these metrics, humans sit towards the less promiscuous side of the spectrum.

So any theory of intense sperm competition is pretty inconsistent with other observed characteristics of human genitals and sperm.

But there also aren’t good alternative theories for human penis shape, when comparing all the primates that do or don’t have similar features.