Was it the fault of Archbishop John Ireland that made Alexis Toth leave the church? Why did he dislike Greek Catholics?
Bishop John Ireland seems to have become a focus point, but really the event is much broader than just him.
A key player? Yes.
Primarily responsible? No.
It should be noted that the Synods and Councils of Baltimore specifically made the Latin rite (as practiced in Baltimore) the official liturgical practice of the American church. You can Google for more information on those councils (they are so brief one can read them all in one sitting).
Thus, canon law for the particular church in the USA forbade the practice of any liturgical rites aside from the Latin. There is no mistaking that the initiative to have the Latin rite as the only one practiced in the USA did come from the American Latin bishops, but they were apparently not educated by Rome about the promises made to Eastern Catholics who might be entering the country, and no corrections were made after the decrees of Baltimore were sent to Rome for approval.
Rome did approve the acts of these councils, so at the time these bishops thought they were standing on good ground. This was also an age wherein conformity was appreciated more highly than diversity, and the Roman Rite was generally thought to be preferred (praestantia ritus latini - bull Etsi Pastoralis 1742AD).
It should also be noted that the Eastern Catholics were erecting church buildings (in many cases, or most cases), without ecclesiastical approval (after encountering refusals by the bishops). They formed associations, or clubs, to raise money for this purpose and asked Eastern Catholic bishops to send them priests.
Bishop Ireland, as well as other bishops, were not about to tolerate these blunt affronts to their authority. I think they thought they could see ‘the camel’s nose under the tent’, so to say.
The church in the USA had already gone through some raw experiences with Trusteeism (probably within the living memory of some of these bishops) and this was beginning to look like a replay of the same crises.
Saint Alexis happened to have been very well educated in canon law and church history (he held professorships). He had an uncle who was the Catholic bishop of Presov, and both his father and his father-in law were also Catholic priests.
He was the chancellor for his Greek Catholic diocese, and director of the seminary. He was plugged in, and probably was a good candidate for bishop himself when his wife (and daughter) had died (unless of course, the fact that he was a widower disqualified him in the eyes of Rome). Instead of a comfortable life in Presov, he chose to be a missionary in America with all of the hardship that entails, made all the more (and to his mind, unnecessarily) difficult by resistance of Catholic bishops all over the USA. I guess he was experiencing cognitive dissonance, his lifelong convictions were not matched by the reality.
Finally, after refusal to recognize his orders and the barrage of insults from bishop Ireland it seems that he acquired new convictions.