There is nothing wrong with being left handed as Umar ibn al-Khattab radiallahu anhu was left handed.
Imam Ibn Kathir (may Allah have mercy upon him) said:
كان ، رضي الله عنه رجلا طوالا أصلع ، أعسر أيسر ، أحور العينين ، آدم اللون
“He (may Allah be pleased with him) was tall, bald, left-handed, his eyes were intensely white with intensely black pupils, and with brownish (tanned) skin”
[Bidaayah wan-Nihayah (10/193)]
Imam Dhahabi (may Allah have mercy upon him) mentioned he was left-handed as well.
Ibn Mandhoor (may Allah have mercy upon him) said about the word (أعسر ):
إذا كانت قوتهما في أشملهما ، ويعمل كل واحد منهما بشماله ما يعمله غيره بيمينه
“A man is called (أعسر ) and a woman (عسراء) if their strength is in their left hand and each one does with their left hand what others do with their right hand”
[Lisan ul-‘Arab (11/146)]
With that said, there are some rulings pertaining to the use of the left-hand:
It is not allowed to Eat with the Left hand
Proof:
وعن ابن عمر رضي الله عنهما أن رسول الله قال: “لا يأكلن أحدكم بشماله، ولا يشربن بها. فإن الشيطان يأكل بشماله ويشرب بها”
Ibn ‘Umar (May Allah be pleased with them) said:
The Messenger of Allah (ﷺ) said, “No person should eat and drink with his left hand for Satan eats with his left hand and drinks with his left hand.
[Muslim]
One Should not Take or Give with the Left Hand
Proof:
عَنْ أَبِي هُرَيْرَةَ، أَنَّ النَّبِيَّ ـ صلى الله عليه وسلم ـ قَالَ “ لِيَأْكُلْ أَحَدُكُمْ بِيَمِينِهِ وَلْيَشْرَبْ بِيَمِينِهِ وَلْيَأْخُذْ بِيَمِينِهِ وَلْيُعْطِ بِيَمِينِهِ فَإِنَّ الشَّيْطَانَ يَأْكُلُ بِشِمَالِهِ وَيَشْرَبُ بِشِمَالِهِ وَيُعْطِي بِشِمَالِهِ وَيَأْخُذُ بِشِمَالِهِ ”
It was narrated from Abu Hurairah that the Prophet (ﷺ) 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 Satan eats with his left hand, drinks with his left hand, gives with his left hand and takes with his left hand.”
[Saheeh Ibn Majah no. 2661]
Shaikh Ibn ul-‘Uthaymeen rahimahullah said:
“Taking with the left hand and giving with the left hand is resembling the Shaytan, opposing the chivalry/manliness, and good etiquette”
[Sharh Riyadus-Saliheen (6/378)]
It is Recommended to Write with the Right Hand and Not the Left
See the Fatwa of Shaikh Abdul-Muhsin al-Abbaad here
One Should Use the Left Hand to Clean and For Other Belittled Actions
Proof:
حَفْصَةُ، زَوْجُ النَّبِيِّ صلى الله عليه وسلم أَنَّ النَّبِيَّ صلى الله عليه وسلم كَانَ يَجْعَلُ يَمِينَهُ لِطَعَامِهِ وَشَرَابِهِ وَثِيَابِهِ وَيَجْعَلُ شِمَالَهُ لِمَا سِوَى ذَلِكَ
Narrated Hafsah, Ummul Mu’minin:
“The Prophet (ﷺ) used his right hand for taking his food and drink and used his left hand for other purposes”
[Saheeh Sunan Abu Dawood no. 32]
Shaikh Abdul-Muhsin al-’Abbad hafidhuhallah said:
“like that when he is wearing his clothes, he begins with the right. Likewise, he uses his right for every affair that is good [such as] when entering the masjid, he precedes with the right, when shaking hands, when taking and giving. All of that is done with the right not the left. The left is used for the affairs which are less than that in terms of removing harm or something belittled”
[Sharh Sunan Abu Dawood no. 10]
And Allah Knows Best
Faisal Ibn Abdul Qaadir Ibn Hassan
Abu Sulaymaan