Meagher was with the 69th New York Militia at First Bull Run and Colonel Sherman was his brigade commander. He viewed Sherman as something of a martinet, probably because Sherman was trying to instill army discipline in the volunteer regiments under his command in the short time available. Sherman, for his part, spoke highly of the 69th New York. The dislike may not have been mutual if Sherman didn't know Meagher, then a junior officer. Or it could have been; Sherman had a short temper.
According to the book, Meagher’s opinion of Sherman became public knowledge, and Sherman took Meagher in dislike. “Deeply” was probably too strong. “Instantly” would have been better word; in the author’s opinion, it was also “permanently.”