To ape someone is to imitate them, often in a mocking way. Most people don't like being aped.
To ape is to imitate, but it can mean a few different things. One type of aping is to blatantly imitate something or someone in every way. That's considered a bad thing because it's so unoriginal — it's a rip-off. Another kind of aping is like a caricature — to ape in this way is a way of making fun or spoofing someone. Either way, you probably don't want to be accused of aping.