Smart alecs guess why I broke no hearts (4,4)

'smart alecs' is the definition.
(both can mean annoyingly clever people)

'guess why i broke no hearts' is the wordplay.
I cannot quite see how this works, but
'why' could be 'y' and 'y' is located in the answer.
an anagram of 'guess' is 'segus' which is located in the remaining letters.
'i' is within the answer.
A single letter 'w' remains which might be clued in a way I don't see.
This explanation may well be incorrect...

Can you help me to learn more?