Praise be to Allah.
There is a prohibition on giving and taking with the left hand in the report narrated by Ibn Maajah (3266) from Abu Hurayrah (may Allah be pleased with him), according to which the Prophet (blessings and peace of Allah be upon him) said: “Let one of you eat with his right hand and drink with his right hand, and take with his right hand and give with his right hand, for the Shaytaan eats with his left hand, drinks with his left hand, gives with his left hand and takes with his left hand.”
Classed as saheeh by al-Albaani in Saheeh Ibn Maajah.
And Muslim (2020) narrated from Ibn ‘Umar (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “No one among you should eat with his left hand or drink with it, for the shaytaan eats with his left hand and drinks with it.” And Naafi’ used to add: “and he should not take with it or give with it.”
Al-Shawkaani (may Allah have mercy on him) said in Nayl al-Awtaar (8/183): His words “No one among you should eat with his left hand” signify that it is not allowed to eat or drink with the left hand, and this prohibition has the sense of being haraam, as is established in usool; it should not be interpreted as meaning that it is no more than makrooh unless there is some indication to that effect in the context. Al-Nawawi said: This applies if there is no excuse. If there is an excuse which means that a person is unable to eat or drink with his right hand, because of sickness or injury and so on, then it is not disliked to use the left hand. End quote.
Based on that, if a person offers something with his left hand for a reason, there is nothing wrong with it, and if he says in that case, “my left hand does not hate you,” perhaps it would be more correct for him to say “my right hand does not hate you”, because he has an excuse for not giving it to you with the right hand, and it does not have anything against you. Or perhaps the meaning is that the left hand also loves you and would like to serve you.
When the one who takes says “Your left hand is like your right,” he means that it does not matter with which hand you give. If there is an excuse there is nothing wrong with saying that, but if there is no excuse, it is wrong to say that because it is contrary to sharee’ah. The left hand is not like the right hand; rather it is forbidden to give with the left hand as stated above.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked: What is the ruling on a man saying to his brother, “Your left hand is like your right,” if he cannot give him something with his right hand, so he gives it to him with his left hand and he says to him, “The left hand does not hate you”? We know that there is no one whose left hand is like his right except Allah, may He be glorified and exalted.
He replied: Whatever the case, this depends on the intention of the one who says it. If he says: “ Your left hand is like your right,” meaning that it is used instead of the right hand when he is not able to use it, in that case there is nothing wrong with it and I do not think that anyone intends to liken any created being to the Creator in this regard. As for the saying “The left hand does not hate you,” I do not know what it means.
Questioner: O Shaykh, this is well known. For example, a person gives something to another person with his left hand, and so that the other person will not be offended, he says, “The left hand does not hate you,” and the one who takes it says: “Your left hand is like your right.”
Shaykh: We have never heard this before. It is not something that we use in our community here. But I do not think that the man intends to liken any person to Allah, may He be glorified and exalted.
End quote from al-Fataawa al-Thalaathah.
And Allaah knows best.