Because she could've been trying to get him to trust her, to let her in under far more devious pretenses. Not that Kara Zor-El had a devious bone in her body, red kryptonite's influence aside.
She wasn't used to flying solo, so to speak. From Winn being there when she first put on the cape to the DEO having her back when she couldn't quite handle a situation all on her own — nevermind all the family and friends that have been a near constant presence in her life outside of her heroic activities. She wasn't used to being alone and frankly, didn't want to be.
Those few cognitive moments she spent soaring through space by herself in that pod were some of the most terrifying of her life. Kara doesn't ever want to feel that alone again.
"Help with what? Because if it's all those gadgets they say you have... I hate to break it to you, but I'm not a scientist. I failed Earth science. Try explaining to your high school chemistry teacher that you got confused, because chemicals don't react the same on Krypton as they do on Earth."