I install all apps through Google Play. Why does Anti Spy still show some of them as “untrusted source”?

That does not automatically mean that the affected app is dangerous. In Anti Spy, “untrusted source” initially describes the detected installation source, not automatically a security judgment about the app itself. On some Android devices, the installer saved is not the Play Store, but for example the System Package Installer. That is exactly what can then appear in Anti Spy as the source.

Open the entry for the affected app in Anti Spy and check under “Source” which installer is actually stored there. If you trust that source, you can add it under Anti Spy > Settings > Scan > Trusted Sources. That way, you stay in control without incorrectly classifying harmless apps too quickly.