I don’t think that the benefit to one party or another is a valid reason to pick a voting system - but one of the features of AV is that it tends to select the least objectionable candidate. Here’s a simplified example.
Let’s imagine we have four candidates contesting a seat - let’s say they represent the Evil Party, the Moderately Bad Party, the Sorta OK Party and the Best of a Bad Bunch Party. Voters for the three non-evil parties would all prefer any non-evil candidate to the Evil one.
Because there’s little to choose between the three non-evil parties, the Evil Party has run a strong campaign and expects about 40% of the vote. The others have been sniping at each other and each will get about 20%.
Under FPTP, that’s bad news - the Evil Party walks away with a big majority and the other three wring their hands about how terrible the rise of extremism is.
Under AV, though, it’s a different outcome. Nobody has 50% of the votes, so there’s an instant runoff.
The fourth-place party - the Sorta OKs, let’s say - has their votes redistributed to other non-evil parties (remember: the non-evil voters don’t want the Evil to get in and would rather elect anyone else). Now the Evils still have 40% and the two remaining parties 30% each. (Exact numbers don’t matter - it could be 40-40-20 and the same logic would hold).
Now the Moderately Bad party is in last place - and all of their votes are redistributed to BoaBB, who now have 60% - and their candidate is elected.
Here’s why I think this is a good thing: it eliminates the need for tactical voting. You could vote for any of the three non-evil parties and be sure that your vote wouldn’t hurt the chances of keeping the Evils out.
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