I agree with the general consensus of the forum here. Obey your mother. You can ask your mother if she'd like to meet him. She might agree to it. But introducing a young man to your family can hint at the desire to have a serious relationship, too, especially if you are having him over for dinner rather than just having your parents be at an event where he happens to be.
I think your mom is on to something. Usually, 19-year-old males don't want to hang out with 15-year-olds. But if she's attractive, some young men might be interested in a romantic relationship with a 15 year old. I have a cousin who was dating a 15 year old when he was about that age. They have been married probably 20 years now.
Think about it realistically. If he isn't dating anyone, do you really think he just wants to be your friend and a romantic relationship with you hasn't even crossed his mind? Even if he is seeing someone, I don't think that's realistic. He might not be rubbing his hands together laughing with a deep maniacal laugh about his evil plans for you. He may be a reasonably nice guy. But your mom can still see this isn't a good situation for you to be in.
You are probably far from the age where you could realistically marry, and it does make sense for your parents to keep an eye on males who want to spend a lot of time with you. Is your dad in the picture? If so, what does he say? You should listen to your mom on this. Of course, you need to obey her.
I remember reading a post on another forum from a woman who said when she was a teenager, she had this uncle that she now sees as kind of sleazy, who was going to pay her way to go with him on this fabulous trip. She was very upset with her parents for not allowing her to go and couldn't understand why. He ended up marrying this really, really young woman when he was older. Now that she is grown up she can see why her parents didn't allow it. Either by evidence or intuition, they could see this uncle could have have had some wrong motives. She couldn't see that about him because she didn't have life experience.
It's really funny looking back on my teens and even in my 20's how naive I was at figuring out people's motives. Now I can read people a little bitter than back then. Even when it comes to reading situations, when you get older, you do get wiser. Your mom can see that something seems fishy to her about this situation. Of course you should obey her. But don't think she doesn't know what she's doing. Just realize that she knows some things you don't and she's developed some intuition that you haven't developed yet.