Fear of making a mistake comes from always playing against high level competition.
In these type of situations wins and losses can all come down to a single player delivering on their responsibilities.
High level competition also forces coaches into player specialization which makes it easier to assign blame / fault if anything goes wrong.
Lather rinse and repeat week after week and you can see why players are more afraid to make mistakes than they are taking risks.
For Girls if a team can be consistent in how they play a position, and everyone trusts each other eventually they'll start taking risks. If risks work out and players don't get burned on position, they'll try being risky more and more often. Eventually they start playing like boys.
I'll start with the carrot for girls. Boys probably know if they go pro, they make great money. MLS avg salary is $530k and the stars make a lot more. NWSL avg salary is $65k and the stars may make more. Trinity Rodman had a supposedly great contract offer of around $275k per year. Trinity Rodman is top of the pack for her age I'm sure.
My opinion is that for girls it is more about fun, chemistry, and the love of competition which is not as strong as boys. Boys love the competion and get majorly rewarded compared to the girls. I told my dd about Trinity's contract and she said "That's it!??" and I was like "that's a lot of money honey!", but she's not stupid.
Women's soccer is gaining exposure and an audience, so things are getting better, but as much as I would love to follow her play everywhere and would be the proudest dad in the world if she went pro, it ain't worth the stress, possible injuries, and/or loss of education it would take to go pro. Better put, she needs to love the competition and the game to have the desire to outperform all the time for herself, because she could get better rewards with a college education.
That said, I think the biggest problem with club soccer is lack of alternative, competitive leagues where they can take risks, play different positions and gain complete skill sets. Winter friendlies and other club team friendlies may help, but they revolve around the team and coaches needs to win and outperform in league. This may help some players get polished into dominant position players, but they most likely become rigid, composed predictable players. Yeah, we have latin leagues and other sources, but I think they need more fun games with different coaches, team mates, etc.
I think our youth women's soccer system creates the issues being discussed here. Women's youth soccer is more of a business than anything imo. The other issue I've noticed with my dd and other girls her age is they want to play with certain girls and teams, etc. Throwing out that if she works her butt off for 5 or 6 more years, she may be able to make $65k per year in the big league doesn't exactly inspire her. She knows how much her mom makes and we're not rich or anything.
Point is I think girls soccer is a social thing and some have the desire to compete and win even without those big rewards. They have to love competing and playing and girls are already a little lacking in this compared to boys imo. I guess they get high school soccer when they get older in addition to elite leagues. Maybe that will help with getting alternative competitive games? I just wish there was a less rigid league they could play where they could play separate from elite leagues. Another problem is you don't want to break their bodies making them run more than 20 miles a week with all the long field games.
You can do futsal and indoor I guess which we do and it helps, but my experience has been that girls don't like to much change or getting yelled at when they learn new positions/responsibilities. It really comes down to the parents, a smart plan, work ethic, and some luck. The saga continues!