As of 2015 it was estimated that methane made up 16% of the human contributions to global warming [0] So, significant but by itself not necessarily worrying.
However, there are a number of other factors that do make methane particularly worrisome. First, the concentration of methane in the atmosphere is going up much faster than CO2, this despite the fact that it decays into CO2 after about 10 years. Further, the higher the concentration of methane the slower its rate of decay, so it stays in the atmosphere trapping heat for longer.
Finally, and most worrisome, there appears to be a feedback loop with warming and methane release from permafrost.
However, there are a number of other factors that do make methane particularly worrisome. First, the concentration of methane in the atmosphere is going up much faster than CO2, this despite the fact that it decays into CO2 after about 10 years. Further, the higher the concentration of methane the slower its rate of decay, so it stays in the atmosphere trapping heat for longer.
Finally, and most worrisome, there appears to be a feedback loop with warming and methane release from permafrost.
[0] https://www.c2es.org/content/international-emissions/