From Michelle Arnold, an apologist at Catholic Answers:
Because man has been given stewardship over animals (CCC 2417), it is perfectly fine for a person to choose to spay or neuter his pet.
Yeah. What she said.
But for the rest of your question.. I’d like to give a brief definition on what it means to be pro-life.
To be pro-life is to seek to guard and protect the sanctity of all human life from the moment of conception until natural death.
Why? Because as Catholics, we believe that human beings are created in the image and likeness of God.
I’d also like to add that even though animals obviously aren’t..

We are still called by God to be stewards of His creation.

Hope that answers your question! I invite you to check out Genesis 1:26-28 if you wanna see the Biblical basis for all of this.
God bless!