I am honoured you’ve asked me to comment, but really, it is up to you to work out your own style for public engagement – polemic, polote, polite but sly, ruthless criticism of everything that exists, and any other number of performative routines.
Whatever the case, late night advice may need a spoonful of salt if you really want it to be taken seriously…
Anyway, I reckon that maybe there are several different ways to tackle this.
Probably good is to say something like:
What I found most interesting about x’s presentation is the way they have reworked concepts of xx to show that x = b.
this gives you a chance to reorder what they have done so as to talk about what you want to talk about, but while still seeming to summarize their key points.
Then say something like:
Of course some people might disagree for the following reasons – a, b and c…list them, in detail… which basically allows you to smash their case, without seeming to have taken sides (good skill to develop I suppose, but sometimes a bit mealy-mouthed when outright hostility is more honest – ah well). Actually, no, that is mean. What you should endeavor to do is to pick apart the argument and material, then stick it back together and return it to the speaker as a reinvigorated project. Saying something like, the implications here are x, y an z – and this was alwyas implicit in x’s presentation.
Then you should leave the audience in no doubt how the something not discussed, or implications not drawn, or assumptions made are, in fact, they key issue at stake – ie, what you are interested in, not what was ostensibly the topic, and it is this which should be the focus of the subsequent discussion.
Then you should come back to the speaker and compliment them for raising such pressing issues, and hope that the discussion of these, as you have set them out, is fruitful.
Or you could just talk generally on what you found interesting. That can meander, but so long as you have a planned start and a distinct end – rather than wittering on more speckled hen warbling than decisive conclusion – and make sure you end. Don’t end with an empty phrase. Just say, …and I think I’ll stop there.
If there are no questions, you then pull out your most popular assertion and ask that as first question,
Sometimes people are too smashed to talk much and it will feel like a damp squib. But when it works, and people feel able to raise questions and join in, well then, viva criticism self-criticism.