Imagine someone-- a coworker, supervisor, or significant other-- approaches you as says, "You've been doing a great job, but..." What comes after the but? Most likely nothing good.
"But" is a trigger word for escalating anxiety. Additionally, there are a number of common "pre-but" phrases that can trigger escalation. For example, the customer service apology ("I'm sorry that you've had the wait so long...) followed by a "but" that negates the apology or precedes an excuse. Additionally, there is the but that follows "our policy.."
"But" is a perfectly useful word when used well. Here is the key to using "but": use it to expand options, not to limit them. For example, "You've been doing a great job, but..I wonder if you been given as much recognition as you deserve, " or "I'm sorry you've had to wait so long, but... is there anything I can do to make you wait more pleasant, such as a drink of water, something to read...?" In these examples what follows the "but" opens new options.
What about situations where "but" is appropriate as a limiter? Leave it out. Instead of, "I'm sorry_____, but or policy______," a more acceptable way to state it is, "I'm sorry_____. [Pause] Unfortunately our policy________."
"But" is a small word, but it can make a big difference.