Engineers, what are good excuses you've used to avoid meetings?

No excuses. Use numbers. Every hour of your time costs the company a certain amount of money. If you include salary, bonus, equity, benefits, etc., the cost for an engineer could be hundreds of dollars per hour. If your manager can't understand that, and ensure you have more time for actual work, it might be time to seek a better manager.

I’m not needed here.

This has no relevance to me.

You know where I sit. Let me know if there is anything you actually need me for.