Silence doesn't sound scary while you're looking at a photo of a path through the woods. Primed by this photo, you are likely to imagine silence as calming or peaceful.
In the middle of an important conversation, this may not be your first reaction to silence. Most often, when we say something significant and get silence in reply, we are rattled. Silence is not processed as calming; it's processed as a warning. The quieter it is outside, the more alarms go off in our brains. "Danger!"
Is silence always a bad sign? Probably not. Think of a time when someone said something and your reaction was "I need to process this." The time when you were processing was best spent in silence (processing out loud is not always a good idea, even for extraverts). This processing time could have been used to do many things: to understand; to tease out an association at the edge of your awareness; to think several jumps ahead; or to disagree.
Disagreement is only one of many options. There's no reason for it to be the one that is top of mind while you are waiting through a silence. But while the other person is processing, your highly engaged mind is looking for an activity. Waiting with a clear head and a clear heart is optimal, but for most of us, it is out of reach.
Here's what to do with your busy mind after you say something important. Take a breath and deliberately be present with what you have just said. Observe the other person closely and non-judgmentally, noticing changes in posture, expression or colouring. Be mindful of your own state by objectively labelling what you notice in your own state. Start at the top of your head and work down, detailing the tension, temperature and movement you notice. As you do, you may notice that you begin to feel calm and curious. Now you can wait.
It is possible that the other person is using the silence to express resistance. While you're waiting, they will think about what to say next. That's probably in your favour, since it is often easier to respond to a specific, reasonable disagreement. They might be trying to understand. You can help after they've found the point where they want to begin. They might be jumping through possibilities, and you will can respond to the one that lands (not the first one that pops up).
Silence is your friend in the woods. It's your friend on a wide open beach or under a wide open sky. Perhaps it's time to make friends with the silence that shows up in conversation.