I just figured out a possible bit of twisty logic while listening to the podcast that I didn't notice on first read through.

I've spoilered this entire thing even though I probably don't need to, just so that you can can figure it out yourself If you want. I think it explains Dumbledore's otherwise incomprehensible behavior in chapter 17.

Cebsrffbe Qhzoyrqber frg hc gur ragver guvat jvgu Uneel'f Nhag, naq ur ncbybtvmrq sbe znavchyngvat guvatf va gung snfuvba. Naq Uneel qvqa'g haqrefgnaq vg orpnhfr Qhzoyrqber vf n ovg qvfgenpgvat.

Puncgre 1: "Naljnl," Crghavn fnvq, ure ibvpr fznyy, "fur tnir va. Fur gbyq zr vg jnf qnatrebhf, naq V fnvq V qvqa'g pner nal zber, naq V qenax guvf cbgvba naq V jnf fvpx sbe jrrxf, ohg jura V tbg orggre zl fxva pyrnerq hc naq V svanyyl svyyrq bhg naq... V jnf ornhgvshy, crbcyr jrer avpr gb zr," ure ibvpr oebxr, "naq nsgre gung V pbhyqa'g ungr zl fvfgre nal zber, rfcrpvnyyl jura V yrnearq jung ure zntvp oebhtug ure va gur raq -"

Cbvag 1: Uneel'f Nhag Crghavn qenax n cbgvba sebz Yvyl Cbggre gung znqr ure fvpx sbe jrrxf, naq gura zber punevfzngvp.

Puncgre 17: "Juvpu ubyqf n greevoyr frperg. N frperg jubfr eriryngvba pbhyq cebir fb qvfnfgebhf gung V zhfg nfx lbh gb fjrne - naq V qb erdhver lbh gb fjrne vg frevbhfyl, Uneel, jungrire lbh znl guvax bs nyy guvf - arire gb gryy nalbar be nalguvat ryfr."

Uneel pbafvqrerq uvf zbgure'f svsgu-lrne Cbgvbaf grkgobbx, juvpu, nccneragyl, uryq n greevoyr frperg.

Gur ceboyrz jnf gung Uneel qvq gnxr gung bnguf yvxr gung irel frevbhfyl. Nal ibj jnf na Haoernxnoyr Ibj vs znqr ol gur evtug fbeg bs crefba.

"Qb lbh frr gurfr abgrf," Qhzoyrqber fnvq va n ibvpr fb ybj vg jnf nyzbfg n juvfcre, "jevggra va gur znetvaf bs gur obbx?"

Uneel fdhvagrq fyvtugyl. Gur lryybjvat cntrf frrzrq gb or qrfpevovat fbzrguvat pnyyrq n cbgvba bs rntyr'f fcyraqbe, znal bs gur vaterqvragf orvat vgrzf gung Uneel qvqa'g erpbtavmr ng nyy naq jubfr anzrf qvqa'g nccrne gb qrevir sebz Ratyvfu. Fpenjyrq va gur znetva jnf n unaqjevggra naabgngvba fnlvat, V jbaqre jung jbhyq unccra vs lbh hfrq Gurfgeny oybbq urer vafgrnq bs oyhroreevrf? naq vzzrqvngryl orarngu jnf n ercyl va qvssrerag unaqjevgvat, Lbh'q trg fvpx sbe jrrxf naq znlor qvr.

"V frr gurz," fnvq Uneel. "Jung nobhg gurz?"

Qhzoyrqber cbvagrq gb gur frpbaq fpenjy. "Gur barf va guvf unaqjevgvat," ur fnvq, fgvyy va gung ybj ibvpr, "jrer jevggra ol lbhe zbgure. Naq gur barf va guvf unaqjevgvat," zbivat uvf svatre gb vaqvpngr gur svefg fpenjy, "jrer jevggra ol zr. V jbhyq ghea zlfrys vaivfvoyr naq farnx vagb ure qbez ebbz juvyr fur jnf fyrrcvat. Yvyl gubhtug bar bs ure sevraqf jnf jevgvat gurz naq gurl unq gur zbfg nznmvat svtugf."

Cbvag 2: Ba svefg ernqvat, V gubhtug "Bu ybbx, n Q&Q ersrerapr naq Qhzoyrqber vf whfg orvat enaqbz."

Ohg npghnyyl, Rntyr'f fcyraqbe vf n fcryy juvpu obbfgf punevfzn. Naq vg'f vzcyvrq gung Gurfgeny oybbq jbhyq punatr vg gb znxr lbh fvpx sbe jrrxf.

Naq...

Puncgre 17: Nu, lrf. V'z fbeel gb fnl, Uneel, gung V nz erfcbafvoyr sbe iveghnyyl rirelguvat onq gung unf rire unccrarq gb lbh. V xabj gung guvf jvyy cebonoyl znxr lbh irel natel."

"Lrf, V'z irel natel!" fnvq Uneel. "Teee!"

Uneel'f Vagreany Pevgvp cebzcgyl njneqrq uvz gur Nyy-Gvzr Njneq sbe gur Jbefg Npgvat va gur Uvfgbel bs Rire.

"Naq V whfg jnagrq lbh gb xabj," Qhzoyrqber fnvq, "V jnagrq gb gryy lbh nf rneyl nf cbffvoyr, va pnfr fbzrguvat unccraf gb bar bs hf yngre, gung V nz gehyl, gehyl fbeel. Sbe rirelguvat gung unf nyernql unccrarq, naq rirelguvat gung jvyy."

Zbvfgher tyvfgrarq va gur byq jvmneq'f rlrf.

Cbvag 3: Cebsrffbe Qhzoyrqber grnef urer vaqvpngr ur srryf crefbanyyl erfcbafvoyr sbe Uneel'f ragver fvghngvba. Gung qbrfa'g znxr nal frafr, hayrff ur npghnyyl unq qbar fbzrguvat .