The right to free speech is at root a matter of property rights. Here is a fun example that I came up with for you to understand how the two relate better.
It is a beautiful Saturday morning at your house in the town of Mayberry as you begin to prepare for a wonderful day of productivity and relaxation. This magical moment doesn’t last for long because suddenly your neighbor interrupts and barges right into your house to demand that you need to repaint your house because its color draws too much attention away from his house. He continues to go on his rant about your house’s paint color. You decide that you do not wish to listen to his nonsense any longer so you tell him to leave your property. At first he refuses to leave so you threaten to call the authorities on him because he is trespassing on your private property, with that being stated your neighbor makes a hasty exit and proceeds to rant at you across the yard from his house. When this does not do him any good he decides to take the matter to the local newspaper. He demands that the newspaper print his story about how your house draws attention away from his house. The newspaper secretary goes on to explain that he can submit a letter to the editor of the newspaper to see if the editor would like to print his story. So your neighbor composes a letter to the editor saying that he has the right to free speech and that he wants the editor to publish his story. When your neighbor notices that his story hasn’t been published in the newspaper he storms into the newspaper editor’s office and begins to rant at the editor about how he has the right to free speech and how the editor is obligated to print his story. The editor, who is completely outraged with your neighbor’s behavior, begins to explain that he (the editor) is the owner of the newspaper and therefore he can print whatever he wants in it. It is private property and the editor is not obligated to do anything with it. The editor then suggests to your neighbor that he start his own online blog or better yet, a newspaper, where he can freely say whatever he wishes. With this news your neighbor is quite upset, but not for long because he immediately goes home and begins an online blog. To advertise his blog and its content he hands out flyers throughout the town. Soon everyone in town knows about the conflict between you and your neighbor regarding the appearance of your house compared to his. Each townsperson also learned about the numerous ways your neighbor tried to get you to repaint your house. Even the big city newspapers began to have interest in your neighbor’s story, enough interest that they decided to print his story! With all of this attention on your neighbor’s house he realizes that his house needs an update- he is going to repaint his house!
That is how the right of free speech relates to property rights.