Wa'alakumussalam warahmatuLlah.
Brother Kalam. Sorry upfront. Not in paragraph format and more than 100 words. I've written this down and then realized your 100 words limit.
1. Evidence from Al-Quran.There is no concept of imamah of the Twelvers in Al-Quran. The best Twelvers can do is by bringing in a very, very vague and ambigous ayah to prove their concept of imamah. And certainly we cannot based our aqeedah on a vague and ambigous dalil, let alone the most important element of their aqeedah i.e. imamah.
2. Infallible guides.They said that human needs infallible imams to ensure that the guidance we received is free from error. This must be so because it is against lutf of Allah s.w.t. if He s.w.t. leaves human being without error-free guidance.
And yet significant majority of the time (since 260 AH or 1,178 years out of 1,438 years or more than 80% of the Islamic history), there is no infallible imam to guide human. Only fallible scholars. So, the claimed that infallible guides is a must has no basis whatsoever when we compared against the past (and still continue) reality. That proves that human's need of any infallible imam after the demised of Prophet s.a.w. is false. Can never ever be proven with the reality.
3. "Mysteries" surrounding the twelf imam.i) There is no sound textual evidence from the Shi'i sources themselves that the twelf imam has ever been born. Their hadiths that tell the story of the birth are all weak according to their own ulama.
ii) Earlier in his "life", nobody knows the name of the twelf imam. In fact, it was forbident to name him until the Twelvers started adopting the view of Waqifi to justify prolong occultation and equated Al-Qaim to Al-Mahdi and hence, the name of Muhammad (I think that happened after 30-40 years of his supposed-birth).
iii) Even though the twelf imam was still in contact with his followers via his 4 deputies for approx. 70 years, a bulk majority of his messages with them were regarding khums and collection of khums and not so much of guiding people. Even Al-Kulayni who lived within this era collected less than 200 hadiths from him out of more than 16,000 he got in Al-Kafi.