It's actually pretty reasonable behaviour by Barclay's and I say that as a bitcoiner myself.

The problem with attempting to do Bitcoin exchange is that there's a sea of hackers out there with access to other people's bank accounts. However, their access is pretty useless because they have no real way to extract the cash. ATMs have limits and require EMV cards which these hackers are unable to clone, and the only other way to get money out is a wire transfer .... to another heavily ID verified bank account. As they also can't beat the ID verification of the banks, they find themselves with access to money they cannot steal.

Enter Bitcoin. They now have the perfect solution: pick a victim Bitcoin trader or exchange, and wire the money to them as part of an anonymous Bitcoin trade. As the trader doesn't check IDs as well as banks do (or don't try at all), the hacker gets the coins without being able to be traced. The bank now has a couple of choices, none of them good:

• They can roll back the transaction leaving the trader with the bill, but this may be forbidden by certain banking rules

• They can eat the loss and block the trader to ensure it doesn't happen again

As rolling back transactions across banks is tricky and usually (always?) manual, eating the loss followed by account termination is usually the easiest path forward.

The solution is for local Bitcoin traders to do ID verification as robustly as the banks do. For that to happen, traders need to be educated and the tools need to be written. Android phones can upload dumps of the e-Passport NFC chips which are digitally signed, so an e-Passport dump + Skype session is usually enough to verify a counterparty to a high degree of confidence (excluding things like stolen passports that the hacker buys because they look similar). But the tools to do this don't really exist right now.

A 17 year old using LocalBitcoins is an uncontrolled risk to the bank. They have uncertain odds of committing money laundering and a certainty of causing dispropotionate chargebacks/reversals. Balanced against this, their business is worth less than nothing: the only reason you can open a checking account at all is to bring them other, more profitable business, in the future, as most operate at a loss.

Terminating their account removes the risk and costs the bank next to nothing.

Banks are very paranoid about criminals using their system, to the point that a slight suspicion triggers their internal police.

That's mandated by laws, government agencies and, to a very large extent, by the public. Look up HN discussions when HSBC got a small-ish fine for not doing enough to stop mexican drug cartels from giving them business. We were demanding jail time for everyone involved.