As St. Paul wrote much of the material that would go on to form the standard NT canon, the reasons for the dislike of the apostle among non-Christians should be obvious, as they disagree with our religion and think it to be false.
And among Christians, too, I think it is also obvious, although a bit different: St. Paul said many things in his epistles which seem to rub certain Christian people or traditions in the wrong way. I remember sitting in on some RCIA classes back when I was Roman Catholic and the women who taught it (in consultation with the priest, but he rarely showed up himself; when he did, they were silent) got to the portion of St. Paul's epistle to the Corinthians when the apostle writes that women should keep silent in the churches. Obviously, the RCC in our day has not
really kept to this rule (depending on how it is interpreted, of course), as women may do the readings and serve as Extraordinary Ministers of the Eucharist in many parishes, and I think one of the women realized that the students would notice this and just sort of quickly laughed it off and said "Heh...you know, that Paul had a lot of strong opinions, and maybe some trouble with women..."
I remember being shocked and not sure how to respond, because of course these women were in charge of teaching the acolytes, so I didn't want to start a scene or anything. So I just thought "Well, that's her way of dealing with that verse" (which it was) and moved on as she did. Still, looking back on it...I dunno...
But I think the sort of sentiment that she voiced is a common enough one among many Christians who would like to see themselves and therefore their religion as more egalitarian than a bare reading of that verse or certain other verses would suggest. So of course since those verses come from St. Paul's epistles, they are attributed to his thinking (read: his misogyny), and he is degraded in their minds as a result. It's sad, but I think that's what I saw at work, and have seen at work since then among Christians who are more 'cutting-edge' and progressive than I apparently am. (And I don't even see that followed as literally in my Church as in maybe some other churches, particularly Protestant ones that might read everything incredibly literally; priest's wives, nuns, and so on have given talks in our churches with the blessings of the clergy -- they just don't play a clerical role of any kind
in the liturgy outside of their place as laywomen unless they're abbesses or deaconesses at a monastery, in the same way that me being a man doesn't entitle me to give the deacon's responses or something, since I'm a layman. I dunno.)