Pursuing happiness and avoiding suffering is synonymous, the reason why is because life should be about fulfilment, being contented and making impact in life that's all that matter.
However as humanity we must strive hard to be comfortable, seeking for happiness but not blindly pursuing it.
Happiness is definitely the demise of suffering, if one is happy then it means they aren't.
In conclusion, we should neither avoid suffering nor pursue hapiness, but strive hard to make impact and be contended.