It would undermine British democracy
The public voted in the majority to leave the EU. This makes the vote legitimate.
The whole reason we ended up with a referendum in 2016 was because David Cameron sought to heal the divide between pro-EU and anti-EU forces in the Conservative Party. This failed miserably. The Conservative Party is more divided than ever and, now, so is the public following a tight-won referendum marred with campaign violations, lies, and controversy.
Has this whole referendum disaster taught us nothing? A second referendum wouldn’t solve the problem of Brexit. The second referendum would only entrench divisions, expand the political divide, and create more irreparable damage in the UK’s political landscape.  Now, the Brexit camp is divided between a soft and hard Brexit. A second Brexit victory would not heal these rifts. While a Remain victory would irk the Brexit side which won a legitimate vote in 2016, and flame tensions.
The first referendum only sewed division because the British public was manipulated, lied to, and was voting blindly without any idea of what a Brexit deal would look like.  Now Theresa May has a deal with Brussels, the public can see what they are voting for and have far more clarity. This will only serve to increase the legitimacy of the second referendum. A legitimate referendum would not sew division but settle the matter once and for all.
The first referendum only sewed more division. The second would do the same. This would be catastrophic for the UK.
The first vote only sewed division because of the circumstances it took place under. A second referendum would have more legitimacy and carry more weight. It would, therefore, heal divisions, not foster them.