1. Question: The Minchas Chinuch (mitzvah 32) asks why are partners liable for working their animal on Shabbos if the Torah says your (singular) animal shall not be worked on Shabbos?
A. By Teruma it says your (singular) grain which the gemara in Chullin 135b says that one is only obligated in the mitzvah of teruma if you own the grain by yourself not with partners. So to by tzitzis it says your (singular) garment is obligated in tzitzis, only if it belongs to one person not if the garment belongs to two partners.
B. The Sforno (Shemos 23:12) says the reason why the verse mentions resting your ox and donkey in the same verse as your maidservant and the convert is because when the animals rest then your maidservant and the convert will get to rest as well.
Answer: Even though the verse sounds like you have to own the whole animal but in logic it is not true because working your animal will come to people themselves working so all animals must rest including if co-owned with a Non-Jew. But this problem doesn’t apply to teruma, tzitzis, peach, or lulav therefore they can’t be owned by partners because the verse indicates they have to be owned by one person.