You are not alone.  My husband and I both experience this, though not as severely as you describe.  It happens in the middle of a call, and sometimes (if neither of us has given up and hung up) the call will resume normally after 30 seconds or so.

I've googled the issue and it's definitely an issue.  We are currently experimenting; he has HD calling off, I have it on.  We'll see if his calls are better. 

It happens on bluetooth in my car, it happens on speakerphone, it happens on a "regular" call, doesn't seem to matter if I received or initiated the call.  Yes, it's frustrating.

Next step - contact Google?  Google Groups is the link to the Pixel Community and searching for "caller can't hear me" yields many results.  You may find an answer, and you can contact Google directly for suggestions or a replacement.