Pastors mean well but they are only human after all, and dont get everything about God and Heaven right. A child has more discernment, I feel than many pastors' and can teach a priest a thing or two!
I also was told this by my pastor-- a very good sincere man. I got the feeling that when he was telling me this, that even he he was being convicted in his heart that his reply to me was not correct. He seemed confused after he told me animals dont go to Heaven.
I later read the words of Christ to His disciples, in His prayer, ".. Thy Kingdom come, on Earth as in Heaven.."
I learned that Earth is a copy of what Heaven is like (minus the man-made pollution and over-development, etc.)
Animals have souls and souls do not die when the body dies. Our spiritual leaders were probably confused with the part of how humans have an additional aspect of a spirit as well as a soul. Our spirit is what communicates with God, and if we choose to submit to God, God's spirit is joined with our spirits in a sort of union- which then influences our souls to want what God wants.
This is the condition of the angels and can be man's condition as well if we choose. It is all via free will.
Where the animals come in is-- our souls- under the control of our spirits- under the control (through love) of the Holy Spirit can then be free to be minister to the animals the way we were intended to.
No more enslaving animals or poaching. no more torturing baby calves so that they can become Veal in our grocer's market. Animals and the entire Animal and Plant Kingdom on Earth would flourish and remain in balance if we fullfilled our callings as 'gardners' and caretakers of this planet. This can only be done if we choose to allow our souls to be subjected under God out of Love (Not duty)
Our spirits then- UNder God-- will control our souls actions , and we will lose desire to be greedy, and bloodthirsty, etc.
This is how it will be like when God's Kingdom is on Earth as in Heaven