OK, it may seem obvious to you that a woman wouldn't want that, but a 31 year old native-born American woman recently wondered aloud here on GAG if she should do that. I don't know how serious she is about that, but this Take is about explaining why it's a bad idea.
Disclaimer: The woman in question is an ex; however, I'm looking at this from the perspective of a guy she'd potentially be matched with and her own as well.
1. Western guys are simply not accustomed to it
When I was a young adult, I experienced three cases of a male relative trying to hook up a female relative of his with me, and not just for a date- it was for marriage. They were all Asian (Korean father and daughter living in the US, Filipino co-worker whose niece lived in the Philippines, and Chinese classmate whose sister was still living in China). I wasn't single at the time anyway, so it was a moot point, but I remember feeling pretty uncomfortable about it and feeling bad for these young women who apparently couldn't choose a partner for themselves. I talked to them so they wouldn't lose face with their relatives, but made it clear to their relatives afterward that I wasn't single.
This isn't something a guy will feel comfortable with.
2. When it is not part of a prevailing cultural norm, it makes the woman look undateable and unmarriageable
A guy is going to wonder why your male relatives are doing this and why you aren't looking for a date online instead. He is going to wonder if there are some underlying reasons why you can't find a partner since women your age get flooded with attention on Tinder and other sites. Besides, what kind of guy is going to go along with this matchmaking?
3. Perception of controlling family members
Whether it's accurate or not, it is an indication that your male relatives control your life and that you are not your own person making your own decisions. That is a dealbreaker for most guys, and certainly includes ones your age and older.
You also want to get a person that you want, and how can anyone else really know what you want?
Furthermore, it's also a really unattractive situation if he has to play fourth fiddle to your kid, your other family members, and your friends.
4. You aren't a young, childless woman
Even in the societies and communities where this sort of matchmaking still occurs, it is generally not done when the woman already is a parent, it's done when she is a young adult singleton, and often a virgin. Furthermore, this sort of matchmaking is on the decline even in places like India where it is a longstanding tradition.
Truth is, a single mom is a much more difficult dating situation than a childless woman. It must be a much tougher sell in a matchmaking situation.
5. What options are out there that you couldn't find yourself?
You live in a tiny town in a rural county. Who would your father know that you don't? Someone he works with? Your brother lives hours away. You don't want a long distance relationship and not too many guys would move to your tiny town to be with you.