Okay, my response:

what matters is not mostly debt in euro terms, but debt as a percentage of GDP

I agree with that.

It's possible to increase GDP rather than decreasing spending, and this will also reduce debt as a percentage of GDP.

Also true. However, it's also more straightforward to reduce spending -- that's pretty reliable. People have a lot of plans for increasing growth, and those don't always pan out. I think that if Italy had maintained a history of growing, then there wouldn't have been a focus on spending reduction.

I'd also add that some ways of generating growth -- like, for instance, having more immigration, are not necessarily popular and one actually has to do them.

what differed was lower GDP growth, and therefore there is a case that GDP should be increased instead [of reducing spending]

I'm not sure that that is true. That is, I wouldn't say that a given country having a given amount of growth also means that one should expect another to do so. It's a sign that it may be possible to do so, but there isn't any country that you can hold up as having the "right" rate of growth that should be adopted by others.

Reducing government spending also reduces GDP, and doing so unwisely may make the debt-to-GDP ratio worse, especially over the long run.

No disagreement, but I don't think that an argument made in the video based on that holds -- the argument was that several areas that saw reductions were a bad idea to see spending reduction because those are areas that are generally considered to have a positive return. Educating one's population may be generally a good idea, but that doesn't mean that it's simply a good idea to spend more on education ad infinitum. There's also a point where one is not making a great return; it's not that there is a fixed, favorable return that one expects to get back every time one inserts an additional euro.