I agree it's nonsensical. My intention was to establish the point that the Fourteenth Amendment, if discussed in the abstract, can lead to abstract conclusions either way. To answer it seriously, you have to look at the relevant caselaw.
Under the current precedents of constitutional law in the US, there is no conflict between progressive taxation and the equal protection clause of the fourteenth amendment. The reason is that income is not a suspect classification, and that the progressive income tax would almost certainly pass the rational basis test.
Background:
The level of scrutiny with which the Supreme Court reviews claims of discrimination depends on whether the victims belong to a so-called suspect class. A suspect class is a group in society whose characteristics are immutable, (like race or national origin), who suffer from a long history of discrimination, who are politically powerless, and who are a distinct group. Earning a high income is, at the very least, not immutable, and it does not make you politically powerless. I also don't think high-income-earners have been suffering from a long history of discrimination -- but the question you're asking is whether progressive income taxes are discrimination, I'll leave this point alone for now.
Because income is not a suspect classification, the standard of review is the "rational basis test". That's a very lax standard of review, requiring only that the basis of the law is not completely crazy. (I don't remember what the court's legal wording for "completely crazy" was.) Progressive income taxes almost certainly meet this standard.