Why are some emails not forwarded to Gmail?

Forwarding is inherently less functional than other solutions, especially if sending to Gmail/Gapps. The reason for this comes down to two things:

  1. If Google deems any significant volume from you to be spam, they will block you for hours at a time. By you, I mean us. For this reason we have to filter outbound email or risk legitimate emails being blocked. They do not give us any choice in that matter.
  2. An email that would be delivered directly to your inbox at Gmail will often be seen as spam if forwarded. This is verifiably true and it forces us to be even more strict in #1 there, the alternative being that our mail service ceases to function reliably.

There is also another key thing to keep in mind here. If you send yourself "test" emails, these will be caught by spam filters nearly every time. These reduce IP reputation for zero gain, as test emails are basically not important by definition, and their lack of valuable data makes them suspicious to effective spam learning algorithms. So always test with legitimate emails. Type up a message to yourself if need be.

Ultimately, if you use forwarding to an external service you will have a reduction in quality of your email service. To some this is acceptable or not noticeable. If an increased risk of not receiving an email is of no concern, there is not much loss there. However, there is a solution that bypasses all problems related to forwarding, and you can find that here:

https://support.google.com/mail/answer/21289?co=GENIE.Platform%3DDesktop&hl=en