Well, it's complicated. But let me point out three big differences which should be enough to start you thinking about things.

First, goals. Financial management at the personal level has the goal of having (at some point in the future) more money. Sovereign governments generally don't have a goal of more money in the future. Their goals are multiple and varied ranging from "stay in power for another year" to "help the economy produce the most it can".

Second, money. Countries usually can print their own money (a big exception: the eurozone) and a household cannot. The personal equivalent would be the ability to write "$10" on a piece of paper and have the store accept that piece of paper and give you $10 worth of goods in exchange.

Third, income. Countries can, within reason, decide what their income (aka taxes) would be. The household equivalent would be for you to tell your job "This year I want to be paid $X" and have it happen, just so.

Given all this, I am not at all sure that there is no limit to the debt/GDP ratio. I rather suspect that as that ratio grows, bad things become more likely (this has mostly to do with public expectations). Of course, even if household finances are the wrong metaphor, that claim is not in any way an argument for large debt/GDP ratios.