I've reading on GPG since yesterday and I have a doubt: the whole system of double key encryption does make sense but it looks to me like either way you are compromising something in terms of security.
If someone sends me an encrypted file using GPG and he/she wants to make sure that I'm the only one able to decrypt it then he/she will encrypt that file using my public key. Now, the only way to decrypt it is to use my private key, which supposedly I'm the only one in the world to have it. So far, so good.
However, if we also want to make sure that there are no forgers and that we're actually exchanging files between us (issue 1) then we would need to encrypt files using each one their own private key. This requires us to share our public keys. But here we go, another problem (issue 2): what if I published my public key on a website/blog/etc. some time ago and I had forgot about it? What if an intruder is able to intercept such messages and by using the public key (that he/she found online) is now able to decrypt files?
The way I see it you have to compromise, and you can't really mitigate 100% both issue 1 and 2. Did I misunderstood something about GPG?
At this point, why not simply try to rely on a 7zip encryption and use a (moderately complicated) passphrase that you both know?