Your coworker's got a point, but it's way less dramatic than he's making it sound. Fast charging does generate more heat in the battery, and heat is the main enemy of lithium cells over time. Studies show that repeated DC fast charging will degrade a battery a bit faster than exclusively using Level 2 home charging. The difference exists, it's real, but we're talking maybe a few percentage points of capacity loss over several years if you're doing it 2-3 times weekly.
Here's the thing though - modern EVs like your Ioniq 6 have thermal management systems and smart charging software specifically designed to handle this. Hyundai isn't selling you a car that gets destroyed by normal use patterns. Your battery's already rated for a certain number of cycles and degradation curve, and that accounts for the way real people actually drive and charge. Most owners see their batteries hold 90% capacity or better after 5-8 years, even with mixed charging habits.
The real practical answer: don't stress about it. Use fast chargers when you need them for your commute. Charge slowly at home when you have time. Your battery will last plenty long enough that the car becomes obsolete for other reasons first. If you want to be extra cautious, try to avoid letting it sit fully charged or fully depleted for extended periods, and don't charge to 100% every single time if you don't need the range - most EV folks keep it between 10-80% for daily use. But honestly, the difference between optimal charging habits and your current routine is negligible over the car's practical lifespan.