My 2021 taxes were rejected due to my dependent so I would like to file alone, how do I do that threw turbo tax ?

First if the dependent should NOT have claimed themselves you should mail in your return to claim the child  and they should amend theirs to unclaim themselves.  You can mail it in now ... you do not need to wait for their return to be processed.

However, if you were wrong and need to remove the dependent  then remove them in the MY INFO section then complete the interview again including the FILE tab to resubmit the rejected return. 

What happened?   Did your dependent file a return that said they cannot be claimed?   If that is what went wrong, you can still file and claim your dependent--but you need to file by mail.  And your dependent needs to amend their incorrect return.

MY DEPENDENT SAID HE COULD NOT BE CLAIMED

Your dependent filed a return without saying he could be claimed on your return and your return was rejected?  AFTER his return has been fully processed and he has received his refund, he has to file an amended return that says he can be claimed as a dependent on someone else’s return.  Amended returns must be prepared on a Form 1040X.  It takes the IRS at least six months to process an amended return.

 Meanwhile, since your e-filed return has been rejected, you now have to print and mail it in to the IRS.  You will not be able to e-file. You do not have to wait for your dependent’s amended return to be processed.  Remember that when you mail a return, you need to include copies of your W-2, etc. with your return.  Use a mailing service like certified mail that will track it so you will know that the IRS received it.

For your dependent:

https://ttlc.intuit.com/community/dependents/help/when-do-i-have-to-answer-yes-to-being-claimed-as-a-dependent/00/1994319

https://ttlc.intuit.com/community/tax-return/help/how-do-i-amend-my-2021-return/00/2544441