Mesh current formulas gives two different results for i2. Why does the first loop provide an incorrect current value?
There is voltage across the current source. Therefore, your KVL equation for the first loop is not correct.
It is logical to find this voltage with the solved \$i_2\$ in your second loop,
\$V_{2A}=12 + 4\times (i_1-i_2)=12 + 4\times 1=16 \ \rm V\$