Takedowns on enemies grant permanent Attack Speed.
WhyGrasp of the Undying
Tahm's incredibly strong slow on [Q] allows him to chase down and trade incredibly well in lane with auto attacks. The stacking health on Grasp further empowers his passive.
More autos = more damage = more health = even more damage
Demolish synergizes well with Tahm's large health pool as well as Overgrowth to empower your ability to punish and take towers quickly.
This slot is highly dependent on lane matchup and enemy composition. If you think you can get away with an easy lane (Maokai etc.) you can opt for a greedier choice in Conditioning.
If you're playing into an oppressive AD top (Riven/Jayce), Iron Skin will pay off big n the early game.
If you're playing into a heavy AP composition, Mirror Shell may be better.
Overgrowth is a rune that allows Tahm to scale, both defensively and offensively, incredibly well. The bonus stacking health further empowers your autos and abilities thanks to Tahm's Passive.
Triumph is a rune that is deceptively good in it's ability to sustain in teamfights. If you're playing frontline and soaking damage, picking up assists will massively heal you to keep moving forward.
Especially during the laning phase, Tahm relies heavily on the ability to take trades by getting as many autos off as possible. The faster autos means more damage from passive, Grasp, and faster passive stacks.