Individuals have no strong reason to have consistent moral values. It does not help the individual much to ponder the question of whether their values are consistent, it is much more valuable for the morals of individuals to be useful than consistent.
And it is more useful to eat chicken and love a pet than to ponder about the local consistency of it.
Having consistent individual values in itself, even philosophically speaking, has little value. A society needs some consistency in it's common values, but even there inconsistencies can be more useful than consistency for the stability of the society.
In philosophy on the other hand, consistency of morals is important, but there is no philosophical view specific to the treatment of animals, because morality is a system for regulating behavior of members of a society to each other, and the animals on Earth are not part of society (and even for humans it's not clear who is part of it, such as embryos or dead bodies).