They probably WERE in your Inbox before being forwarded.
Under Settings, what do you have it do with the message after forwarding it?
Do you "delete Gmail's copy?" They get into the Trash only if you (or a
Filter or Forwarding) put them there.
The ones that automatically go into the Spam folder would not be forwarded.
Gmail's spam filters do sometimes require human (your) intervention. They
don't train themselves to new spam patterns; you need to (re)train them, by
clicking on the Report Spam button. If you never login to your Gmail
account, you lose that opportunity to improve and update the spam filters.
Andy