Why do mesons decay? Why do mesons decay shortly while baryons are more stable? And why do mesons decay, meaning that there are unstable, while they formed because meson is more stable than the two corresponding quarks? This looks to be self-contradictory.  
 A: All hadrons, except the proton, are unstable. Supersymmetry theory claims that even the proton is unstable, although the experimental evidence for that is not good, and if proton decay does happen, the mean proton lifetime is probably greater than $1.67\times 10^{34}$ years.
Every meson consists of a quark and an antiquark. When you have a matter particle in close proximity to an antimatter particle like that, it is bound to decay sooner rather than later. Baryons consist of 3 quarks, or 3 antiquarks, so they don't have that instability due to having matter combined with antimatter. Still, some baryons have very short mean lifetimes, especially those composed of the heavier quarks, or of quarks in excited states.
Quarks aren't exactly unstable, but they can change flavor, via the weak interaction. For example, a free neutron is unstable, with a half-life of around 611 seconds. One of the down quarks in the neutron converts to an up quark, turning the neutron into a proton. During the down-up conversion, a $W^-$ weak boson is emitted, which quickly decays to an electron & an (electron) antineutrino. 
However, quarks carry a color charge, so they are subject to color confinement. That means we can never observe a single or composite particle with unbalanced color charge, we can only observe composites where the total color charge is neutral, eg a baryon with red + blue + green quarks, or a meson with for example a red quark and an anti-red antiquark. The color charge is rather dynamic, so in a fairly short time our red + anti-red meson could be a blue + anti-blue meson; that color change essentially has no effect on how the meson interacts with other particles.
A: Mesons, for example the pion, decay because they are made from a quark and an antiquark. Particles and anti-particles don't get on very well, so as with an electron meeting a positron, they quickly annihilate or decay. A negative pion disappears when it emits a muon anti-neutrino and a negative muon. The neutron, which is a baryon, doesn't contain an antiparticle, but nevertheless is unstable outside the nucleus and decays with a half-life of 10.5 mins. As long as it remains within a nucleus, the neutron is stable and will never decay. 
