Confused regarding tooth extraction

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I had a relatively small jaw when I was a kid, and my mouth was overcrowded. The dentist has advised to pull out some of the teeth, but my mother didn't agree to that as she was scared. So, it was left untreated.
Now, my daughter is having the same issue. She is five years old and has a very small jaw. Her baby teeth are crowded. She has lost her two front teeth and the adult ones have squished in there. I took her to a dental care clinic in Barrie and the dentist told that she needs a tooth extraction.
I am loath to teeth extraction, just like my mom. It was just drummed into me that tooth extractions are unnecessary and are dangerous to the jaw structure, which can lead to the "droopy mouth" syndrome. When I discussed my fears and concerns with my husband, he told me that my concept was utter foolishness.
I am confused about this and requires clarification. What are the consequences of having a teeth extraction? What can be done to avoid overcrowding of teeth? Is genetics a factor?