Methane doesn't have a half-life, but you are correct it doesn't stay around forever. In about a decade it will react to become carbon dioxide and water vapor, which both contribute to warming themselves.
Scientists know this when they state that over a 100 year period, methane traps 32 times more heat than CO2 [1]. This is the number widely cited. Over a 20 year period it is even worse: 104 times greater! Considering we are trying to drastically reduce the human contribution to global warming over the next 10 to 20 years, methane is a great thing to focus on.
Other thoughts:
It is interesting that the cow population only increased 35% since 1960 according to that source. But what about the methane per cow? Some quick searches suggests the slaughter age may have decreased from 3 years to 15 months during that time. They are growing much faster, fed grain that leads to the methane burps. At a minimum several times more emissions per cow.
CO2 only sticks around for 100 years, by your line of reasoning we should just shrug that off too?
Scientists know this when they state that over a 100 year period, methane traps 32 times more heat than CO2 [1]. This is the number widely cited. Over a 20 year period it is even worse: 104 times greater! Considering we are trying to drastically reduce the human contribution to global warming over the next 10 to 20 years, methane is a great thing to focus on.
Other thoughts:
It is interesting that the cow population only increased 35% since 1960 according to that source. But what about the methane per cow? Some quick searches suggests the slaughter age may have decreased from 3 years to 15 months during that time. They are growing much faster, fed grain that leads to the methane burps. At a minimum several times more emissions per cow.
CO2 only sticks around for 100 years, by your line of reasoning we should just shrug that off too?
[1] http://science.sciencemag.org/content/326/5953/716