"Lower rebirth" -- Are animals really "lower" than us? I love most aspects of Buddhism but I can't agree that animals have a "lower" rebirth than us. Dogs for example sometimes have enormous love and compassion for their owners, even if they are being terribly mistreated. I am a vegan because I love animals; animals do not harm us, yet humans routinely kill animals for their own sensual pleasure. The dairy and egg industries are also very cruel -- all those male chickens being killed! And how female dairy cows are always kept pregnant or lactating through artificially insemination. It's human cruelty that keeps them in their difficult position. Saying "It's just their bad karma" is in my opinion a way of weakening your own karma.  

Many animals are somewhat psychic -- they sense things that humans can't. Personally I would rather come back as an animal than a human. They seem more peaceful, humans are constantly thinking and doing and stressing about things. So can I still be a Buddhist, with these beliefs?
Lower is not meant as a moral judgement nor a pejorative in this case. It is meant simply as a statement of the more dire predicament most animals are in compared to most humans. There certainly exist individual dogs, cats, horses, pigs, donkeys, monkeys, deer, sheep, cows, chickens, fish, birds, reptiles that are more compassionate and exhibit virtues superior to individual humans in this very life. However, generally speaking humans have a greater capacity for understanding dharma and opportunity to practice. Most animals are subject to base instinct and spend the vast majority of their time just trying to survive. In this sense it is called the lower or less fortunate realms.