I should know my history, but am not very good at it…
Pope St Pius V was Pope at the time of Elizabeth I’s reign. At this time there was significant turmoil within the British isles due to the reformation, and other things. Scotland was now ruled by a Catholic monarch, and Elizabeth I continued the spirit of the reformation, oppressing Catholics. You see there had been Henry VIII, who was okay, save that he split the Church from Rome. The Church under Henry VIII was essentially still catholic. But then King Edward came along, who was staunchly protestant. After his death (save for the 7 day reign of Queen/Lady Jane Grey) Queen Mary restored Catholicism, but when Elizabeth came to the throne the Catholic Church was once again persecuted.
From my understanding of the subject, it was for the persecution of Catholics, the growing political intrigue against Scotland, and the Queen’s own heresy. The Papal bull
Regnans in Excelsis declares Elizabeth I a heretic, excommunicates her, and declares Queen Mary of Scotland to be Queen.
Hope this helped somewhat! There is more info on Wikipedia
here. It’s a rather complicated time in English and Scots history.