It is Kurolo who abandons his son.
The one who abandoned him was Chrollo's mother, Sayoshis.
The instigators were Sayousis' friends, Fulis Jin and his close friend Xiang Xiang.
His abandoned son chased his mother and left his hometown, that's all.
He lived a life of dire straits, life was worse than death, and he complained about everything but his mother. . .