It makes me a little sad that Birthing Pod didn't get any of its strategies hurt. Being able to throw in silver bullet answers is one of the reasons green sun's zenith got banned, it made it the overwhelmingly powerful strategy so that other midrange decks didn't have a reason not to also go that strategy. Also, having 2 card combos that do infinite damage allows the deck a quick avenue to beat stuff that can stop its midrange plan without diluting your deck too much makes it impossible to stop with just one strategy.
Honestly the best thing you can do to beat it is not care about it and just combo out yourself (splinter twin) or try to kill them in the first 2-3 turns before they can get their advantage going (affinity), but this has left modern in a pretty crappy place right now. Affinity is like the dragon stompy of legacy, where variance will bury you or allow you one to two big tournament wins.
I think the problem is pod isn't played enough for people to see why it's the reason for modern being a "slow combo" format. Even though it is
the most played deck in the format, it doesn't necessarily comprise the majority of the
top 8's (2/8 in that case, but 7 of the top 16 lists). The problem is that the card advantage it buries you under (if you don't just ignore it and combo yourself, like Scapeshift + Twin) makes it impossible for regular midrange style decks to handle in time to kill you. Only a single BGx list made top 8, 2 in the top 16.
To stop Pod without a combo, you have to go the UWR control strategy with upwards of 15 removal and additional countermagic.
I do think the deck is oppressive and banworthy. The worst thing is their ability to cast a turn 2 Birthing pod relatively easily, which makes it near uncounterable and being an artifact is almost impossible to kill. If they print an Abrupt Decay that hits 4 cmc cards or some better removal for artifacts that doesn't just suck without being in your deck,
maybe pod would be more handle-able, but as it stands it's just too good.
Anyway, rant aside, the best card to fight that deck right now is Aven Mindcensor and hoping that they don't draw an abrupt decay. Aside from that I'm having fun with
Damping Matrix, which also conveniently gets hit by Abrupt Decay (like
Grafdigger's cage,
Stony Silence,
Rest in Peace, and just about every other card you'd hope would shut their strategy down).