I am naturalized US citizen from the Philippines. Can I use my Philippine passport to travel to Brazil?

It's because the Philippine passport holders do not require a visa traveling to Brazil whereas US passport holders do.

If you have dual citizenship you can, but to get back in here you will have to show ability to come in, and since that is your US passport, it could be confusing.

However, it is what it is.

People do that to go places Americans passports aren't accepted, so it does happen.

For as long as your Philippines passport is current and valid for the duration of your stay in Brazil, then there is no problem. Bring your US passport to re-enter the US after your trip.**