You take the following things as premises: a.) Humans tend to reproduce, often above-reproduction level b.) Humans usually tend to optimize their well-being c.) Well-being of individuals of your own species is more important than well-being of other species
The first two should be uncontroversial. The third one is not uncontroversial but still the foundation of most legal systems worldwide.
The argument goes: More humans need more resources. Each generation uses more resources than the previous generation, due to (b). Even if you could educate everyone to use less, due to (a) you would still have to provide more resources. Better technology allows more efficient generation of resources with less impact on the environment. Thus if you care about the environment/whatever, technical advances are a good thing. You could also try to kill humans/don't allow them to reproduce but this clashes with (c) and basic decency.
Also: You will never convince a non-marginal amount of humans to give up pleasure for some greater good.
- Cruelty of meat production will be solved by artificial meat, not by a tiny percentage of vegetarians. - Global warming will also be solved by clean energy, not by using less energy.
What Hassabis is hinting at is the possibility of using AI to advance crops (GMOs) and materials in way that allows efficient provision of more stuff for more people. It is far more likely that these efforts yield fruits than that you convince 8B people to constrain their consumption (we've tried the latter for many years now: If you're aware of any progress made so far I, please share).