There are a lot of errors in that article. Like line 1, the idea that foreign students get jobs before Americans do. Quite the opposite in real life. Go to any school, and see the employment rates in that school for US vs foreign students.
Also H1B pays FICA taxes, that exemption is only for OPT. The OPT exemption can be easily removed.
That first point is not comparing students, it is saying that the H1B visas issued that year all have jobs lined up (which is a requirement of the visa). Those jobs are what the new graduates would normally be competing for.
And you have to apply to get that job. And the vast majority of companies would prefer a US citizen or an LPR for that job, because there is no guarantee that you will get the visa approved.
Grad students (foreign and non-foreign) also don't pay FICA (or at least, they didn't when I was in grad school). Not that it matters much, grad student pay is nothing to dream about.
Also H1B pays FICA taxes, that exemption is only for OPT. The OPT exemption can be easily removed.