Our cars use an earlier version of Homelink than what is produced today. My 2012 Honda's Homelink can open both garage doors, but the Crossfire's Homelink can open neither. That is because my garage door openers are more modern, and use a newer version of Homelink software. I have read lots of suggestions as to what worked for the specific poster, but none worked for me, as the poster could have had any garage door opener from any year.
Homelink's web site lets us type in which opener we have, which car, and then tells us what we need based upon the software used in Homelink in different years. For my 2012 Honda, the website shows the onboard Homelink is compatible with my modern garage door opener. For my 2005 Crossfire, the website says I needed a bridge shown in the post above. The bridge is basically a software translator from old to new. I just installed the bridge and have put the Crossfire's Homelink in service.