。
I really can't just throw it away.
Literal
Really throw-away [reason-わけにはいかない] [informative-よ].
~わけにはいかない ('can't afford to, mustn't') expresses that something is impossible due to circumstances, social pressure, or moral duty — not mere inability. 捨てる ('to throw away') is what the speaker feels they cannot do. よ adds assertion.