Ever have someone call you in the middle your busy day and then they launch into something completely unrelated to what you're doing? It's disorienting. It's sometimes abrasive. It can feel like someone busting the door down at your house while you're having dinner.
On the flipside, do you ever do this to others?
Most people will allow you to continue on once they've answered the phone because they don't want to be perceived as rude by dismissing you, but in fact, if you've completely interrupted them, they're only going to catch half of what you say, at best.
Conversationally, how do you politely knock before you enter someone's world? How do you ready someone to hear you before you begin?
It's really about expectation and permission.
Most people don't need much time to switch gears. If you help them with this, you'll have a more successful conversation and both of you will listen better to the other.
Start your part of the conversation with something that respects them and allows them an easy out.
"Hi Sue. It's Brett. Is this a good time, or a bad time, to talk?"
"Hi Jason. This is Brett, and I wanted to know if you have a few minutes?"
By starting with the question and suggesting that it's okay to delay the conversation, you honor their world. What's more, if now is a good time, they've given you permission to proceed, and mentally, they're more engaged, having set down their things, so to speak, to really hear you.
The more you help others succeed at listening, the better your relationship will be.