Hello kidush,
Welcome to Apple Support Communities!
If we understand your post correctly, when you place your cursor on some text on a webpage and click search web it always opens in Safari even though you have your default browser set to Chrome. We'd like to help!
Let's check two settings on your iPhone.
Settings > Chrome > Default Browser App. Make sure this is set to Chrome.
Next, Settings > Safari > Default Browser App. Make sure this is set to Chrome as well.
Let us know if you have any questions.
Thank you for using Apple Support Communities.
Take care!