You and others may thing you are being pedantic, but you are not. You are simply wrong.
If I get a Rolex watch as a gift, and a friend asks how much I paid for it, I would not be wrong to say "I got it for free." The fact that someone else paid for it doesn't change the fact that it was free for me.
The fact that someone paid for it is not contradictory to it being free.
In a later comment you say "Well, if we can redefine free to mean "I will let someone else pay for it" or "I will pay for it at some later date", then sure..."
"I will let someone else pay for it" is true, and it is not redefining free. It is free and someone else paid for it. Don't construct a world view where they are opposing each other.
And no, you will not pay for it at some later date. That's a loan, and is what we in the US often do for school. You may pay the tuition for other students who come after you, but there are usually ways to opt out of that with no penalty. And even if you do end up paying for others, it is not a reciprocal transaction. You are not paying for others' education because you received a free one. You would still pay for it even if you opted out of university.
Yes, the education is free.
Why am I taking the time to write this out? For two reasons:
1. Often (but not always) people like to make this point because they want to have a discussion of the wider economic system, and often about the pros and cons of that system. Yet you have not really made an effort to have that discussion so it may not have been your motivation.
2. If we go with your notion of what "free" means, then we should be consistent and realize pretty much nothing is for free. A plank fell off my fence. I could have paid someone to fix it, but instead I took a hammer and nails and got the work done for free. "Oh no!" says the listener. "Don't think you got it for free. You paid for it in labor, and in buying the hammer and nails." You respond with "Well no, I found the nails and hammer in the trash - someone was moving out". "Yes, but he paid for it, so still the work you did was not free."
These conversations never happen in real life. No one disputes that I did it for free.[1] So why do we allow ourselved to get sidetracked with the issue of whether health care or education is free - especially when it is not the purpose of the conversation at hand?
Well, OK - some people will question whether my time was worth it vs just paying someone, but that's the extent. And the analogue to "free" education would be "No it wasn't free. You spent 4 years of your life there - you need to consider the opportunity cost"