Just as Legolas could not see his own future, he could not see Estel's.
The prince did not like the direction the conversation was heading.
He could sense what Galadriel was hinting at.
Something bad would happen to Estel if he died now.
The mirror was controlled by her magic, so if the Lady wanted to, she could project whatever images she wished.
The mage knew well enough that whatever he saw could not be trusted.