What is the detailed analysis of the first opinion that states that a pregnant or nursing woman only has to make up the missed days?

This opinion, which is endorsed mainly by the Hanafi and Maaliki schools, is the opinion that is accepted by the majority of the scholars. The general evidence supporting this position is in the hadith:

Narrated by Abu Dawood, al-Tirmidhi, al-Nasaa’i, and ibn Maajah:
The Prophet (pbuh) said: “Allah has relieved the traveler of half the prayer and of the duty to fast, and He has relieved pregnant and nursing mothers (of the duty to fast).”
Classed as saheeh by al-Albaani in Saheeh abi Dawood.