Just to give some sort of background:
The seven letters listed - 1 Thessalonians, Galatians, 1-2 Corinthians, Philippians, Philemon, Romans - are the ones most or all scholars accept (or not dispute, at least) was written by St. Paul himself. Earlier scholars (ones from the 18th-19th century) in fact accepted fewer letters, but as time went, more scholars began to reconsider a few other letters and accepted their authenticity.
Scholars are evenly divided between Colossians and 2 Thessalonians: some don’t think they wer really written by Paul, others argue that they were. Much of the debate, for Colossians at least, really rests on the vocabulary: the language (word usages, turns of phrase) doesn’t seem to match Paul’s language in the other, undisputed letters. (But this in itself is a disputable argument.) 2 Thessalonians has a slightly stronger claim for it, but then again some argue that certain parts of the letter (2:13-16 or 5:1-11, for example) were not really by Paul but later interpolations.
A majority reject 1-2 Timothy, Titus, and Ephesians as authentic.
For Ephesians, the argument is really that it’s too vague: it really reads like a generic circular letter (there are no references to people in Ephesus, or any events Paul may have experienced there), and it seems that the words “in Ephesus” is a later interpolation. (Marcion in the 2nd century even thought that the letter is actually the now-lost letter to the Laodiceans.) And again, there’s also the issue of language: it is argued that it doesn’t really sound ‘Pauline’ - more so than Colossians. (It does however show more similarity to later Christian literature.) That, plus the fact that Ephesians shows a huge similarity (in language terms) to Colossians, while at the same time, showing differences from Colossians (the theology is more developed in Ephesians, for one).
As for the Pastorals (1-2 Timothy, Titus), again, the issue is language: the author sounds more like a quiet, meditative Hellenistic philosophical author than Paul in his other letters: vivid, lively, occasionally meandering in dramatic arguments and emotional outbursts against his opponents. Plus, the rather developed church organization envisaged in the letters sound suspicious to these scholars: they think that the system only really became developed and standardized after the time of Paul and the apostles.
Hebrews meanwhile obviously isn’t really considered a Pauline letter - even in antiquity Christians were divided about it. It’s the one letter where the difference in style is very obvious, whereas the others are honestly disputable.
That’s pretty much how their argument goes.