Is there a halachic or hashkafic problem with eavesdropping? Maybe it could be like reading another's mail which Rabenu Gershom made a gezera about.
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A few potential angles to say it is a bad idea:
Since mimetic tradition is a strong source in Jewish thought: My mother told me it is bad middot.
Rashi on Bamidbar 24:5 says that Balak was praising Jewish homes for not having one door face another. This creates the notion of privacy within one's home being a good thing. Eavesdropping, as a violation of that, would then be a bad thing.
Finally, there is a notion of keeping secret those things which are said in secrecy. This is derived from Vayikra 1:1, from the superfluity of the word "leymor". The Gemara Yoma 4b says anything which a person is told, he may not repeat unless he is told that he may. Eavesdropping is of course a violation of that notion.