How we can explain Mr. Lantin's hate in the first part of the story?"The Jewelry" by Guy de Maupassant

I think you probably mean the second half of the story, for M. Lantin was smitten with his wife from the moment he first saw her until the day she died--and even a little after.  He loved her, wanted her to have nice things, and encouraged her to go to the theater even if he did not accompany her.  She loved him, too, as "she would throw herself into his arms, and kiss him affectionately" some evenings when they were home together. There is nothing but love, it appears, for the first half of the story.  The change happens when his wife dies.

Once she's died and he's broke and life is a "struggle," he takes one of her necklaces to a jeweler, hoping to get a few francs for it. Instead, he discovers the jewels are real after getting a second opinion. The second jeweler knows exactly how much the necklace is worth (12,000 to 15,000 francs) because it was bought at his store.  While that is a surprising and even exhilarating thing for him to find out, he is soon struck with the realization of what his wife must have been doing throughout their supposedly happy marriage.  "The earth seemed to tremble beneath him--the tree before him to be falling; he threw up his arms, and fell to the ground, unconscious."

From here his life deteriorates quickly.  He does sell all the jewelry (who would want to keep it, given the circumstances?), but he is humiliated by the workers at the store.  They knew perfectly well his wife had been unfaithful to him; one employee even has to leave the room to hide his mocking laughter. 

He's angry because his wife cheated on him; he's angry because he didn't realize it and probably should have; he's angry because he made it even easier for her by sending her to the theater alone (or so he thought); he's angry because he'll never know if she really loved him; he's angry because he was humiliated by people who don't even know him...and the list goes on. 

The anger hinges on the fact that his wife was unfaithful to him and he was clueless.  I think we can all understand, to some degree, what that must feel like and can empathize with his anger.

Unfortunately for him, Monsieur Lantin grows quickly into a bitter and complaining man who lives a life of dissolution--an "I'll show her" kind of thing.  "Six months afterward, he married again. His second wife was a very virtuous woman; but had a violent temper. She caused him much sorrow."

The irony of the last sentence is delicious: his first wife was a liar and a cheat, but they were happy; this wife would never lie to him or cheat on him, but she made him miserable.  His anger, it seems, is justified.