The reject email should say why.  A common reason is the wrong AGI.

ENTER 0 FOR AGI. The IRS took a long time last year to process 2020 returns so the AGI didn't get entered in time.  Especially if you mailed it.  That works for most people. See,
https://ttlc.intuit.com/community/rejections/help/what-if-i-entered-the-correct-agi-and-i-m-still-ge...

How to correct the AGI in the Online version
https://ttlc.intuit.com/community/agi/help/where-do-i-correct-my-agi-in-turbotax-online/00/26311

If you can’t get it to efile you will have to print and mail it.
https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online...

Be sure to attach copies of your W2s and any 1099s that have withholding on them.  You have to mail federal and state in separate envelopes because they go to different places.  Get a tracking number from the post office when you mail them for proof of filing.

Rejections do not come from TurboTax.   Rejections come from the IRS.

You received an email that we cannot see that tells you why your tax return was rejected.  

Some rejected returns can be fixed and re-filed.  Some have “un-fixable” reasons for the rejection and have to be mailed instead. What is the rejection code or rejection message? 

 If it was rejected for AGI—-be aware that many 2020 returns took so long for the IRS to process that your 2020 AGI might not be in the IRS system.   Try using zero instead.

If filing with zero is rejected then file again but select the option that you did not file last year.  The IRS does not see that question and it will allow you to e-file with no AGI question.

https://ttlc.intuit.com/community/agi/help/where-do-i-correct-my-agi-in-turbotax-online/00/26311

If that does not work and you still cannot e-file, then print, sign, and mail your tax return.