The big advantage of nuclear is that all your waste product is largely contained on site in a local container. Coal combustion launches stuff into the atmosphere that's hard to get back.
Climate change is tough because, while I firmly believe the evidence demonstrates the human race's hand in exacerbating it, the effect can be hard to differentiate from background noise over the period of time we're studying (and can study due to investigative limitations). That is, we just haven't been keeping records long enough to correlate data to a firm degree of confidence.
Engineers like "damped systems". Put a weight on a spring, and let it boing. It oscillates up and down. If it didn't have any "real world" effects like air drag or thermal metallic fatigues, it'd boing forever in a predictable, sinusoidal (the operative word) pattern - up and down. In the "real world", those effects we know will eventually cause it to stop boinging and come to rest at a constant position - it's steady state resting place where the upward pull of the spring exactly counteracts the downward pull of gravity. Those "real world" forces "damp" the system so the oscillations decay and arrive at that final point.
Steering a cruise ship is analogous. When you want a cruise ship to go a different direction, you have to start making the turn in small movements well ahead of the turn. It'll take a while to see any change in the ship's course. You have to stop turning well in advance of the intended course and let the ship's momentum carry it to that point. If you use large inputs, typically too late, the ship is just going to flounder around.
Climate change and economic systems follow these time delayed inputs. You have to make changes well in advance of your intended effect, which requires some imperfect measure of prognostication.