So I‘ve usually said something like: “what’s the best time for you? You can also pick a time here if easier:”
But maybe there’s a product experience that can solve / prevent this problem.
Anecdotally, people ~40+ do take it personally as parent comment mentioned. It's a "your time is more important than mine" feeling by putting the onus on them. Around ~40% of the time, more senior people have ignored a booking link, and responded with times that work for them, requiring additional messages to confirm everything.
People under ~40 almost always use the link without issue, and usually send a confirmation email or message. People <30 don't respond to the message, just book and I assume we're good to go.
Now I use a "Let me know if there's a good time for you. Otherwise, here are 3 slots and my booking link" message.
Even had to make a Google Sheets app script to list my open 1.5+hr slots for the next 3 weeks to help with pre-populating that.