No, you need to break it down: Who has a love of cooking? Her boyfriend. Does she share it? No. So it means: he has a love of cooking, but she does not share it. i.e., she does not have a love of cooking. So a simplified version of this sentence: My boyfriend loves to cook, but I don't. She might love her boyfriend's cooking (she gets to eat the food), but she doesn't love cooking herself.