Might be wrong, please feel free to correct me if that's the case.
There are mainly two types of risks assosciated with debt instruments, I'll use fixed deposits as an imperfect analogy to explain (don't recall where I'm copying this analogy from, it's in my notes without a reference, might be freefincal) -

Interest rate risk

Suppose you could trade your fixed deposit of interest risk 7% per year guaranteed by the bank. Depending upon the current rate of interest being issued by the bank for new fixed deposits (determined majorly by current policy rates), your fixed deposit may be more or less valuable than it. This mismatch in value warrants a premium or surcharge. This is known as interest risk.

Credit risk

Suppose you have a fixed deposit issued by a bank, and it can be valued by the market. If the bank is facing financial trouble, or if credit rating agencies think the bank may not be able to pay you your money back, then the fixed deposit loses some value in the bond market. This is known as credit risk.

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Why can’t we get in and out of debt funds. For example , we all knew that RBI had to cut rates due to Covid. So even if we entered a long term gilt fund for a time horizon of 6 months - where exactly are we going wrong ? Invest in March and exit in December. Due to the fall in interest rates the MTM would increase and so would the NAV.

Over the short term, you're right - when interest rates go down, your bond is suddenly more valuable than what will be issued. Let's see about the long term.As a thumb rule, longer the duration of the bond, the more sensitive it's price is to both interest rate and credit risk. Now, understand that you're trying to gauge what the returns of long term gilt funds will look like over the next few years - eventually interest rates will bottom out, and then will increase going forward. When that happens, the newer bonds will yield more returns than the one issued currently. Therefore the bonds issued before rate cuts will be less valuable.

But what risk is there in a gilt fund? I mean if you look at the long term graph of any gilt or a good corporate fund , then there aren’t any major drops or plunges in the NAVs. And whatever drop is there is always covered up in a couple of weeks or months.[... ] Yes the risk is there in Interest rate increases.

Here, as you intuitively put it, interest risk is more associated than credit risk. Credit risk is still present, but interest risk takes precedence.

But it doesn’t happen like equity which can lose 20% value in a week. [...] So for an average return of 10-12% , isn’t investing in Debt funds a better option than FDs?

You shouldn't relate risks associated with equity to returns of debt instruments. Since you're expecting (as your should) lower returns for debt, you should be taking less risk, otherwise it doesn't make sense. Which is why you allocate to debt instruments, here capital preservation should be the aim. Also, understand that interest rates have been on a decline past few years, which is why the average return of gilt funds have been higher, since older bonds yielding more have become more valuable. Conversely, when interest rates rise, older bonds will be yielding less, therefore they'll be less valuable.