Because Minecraft is digitally signed. META-INF contains the manifest, but also a signature file (
MOJANG_C.SF) that accounts for all the files within the JAR and their checksums, and Mojang's actual signature (
When that signature checks out, you know it wasn't tampered with and comes from a trusted source (in this case, Mojang). When you do tamper with it (by installing mods), the signature is invalid and Minecraft won't start at all.
By deleting the META-INF directory, you remove the signature completely. Depending on your security settings, you might get an "unknown publisher" warning, but you'll be able to run it.
More detailed info: JAR File Specification