There is no compelling reason why dogs bow their heads, except when they use our senses after they have gone to the carpet. According to Psychology Today, this may be related to vision.
Dogs are emotionally developed. They have an insightful ability to understand our body language and voice signals — even the slightest intonation or special words they perceive with fun. As part of the arsenal of “reading body language,” dogs constantly “read” our faces to determine their emotional state.
According to Stanley Koren's research, dogs put their heads down to better see our facial features, as their muzzle covers the lower half of our faces. Along with our eyes, the mouth is an important part of human emotional expression, especially for dogs that respond to whether our teeth are visible or not. If you bring your hand to your nose, you will see how the dogs approximately see.
Coren's research included an online survey of 582 people about their dogs. 62% of respondents said that the dog regularly bowed his head when talking to her.
Only 52% of owners of short-sided dogs (such as pugs or bulldogs) said that their dogs bow their heads. 71% of owners of long-sided dogs (such as greyhounds) confirmed that their dogs bow their heads when talking. The statistical gap between the long-sided and short-sided dogs allowed Koren to conclude that the inclination of the head partly affects their visual perception.
However, the percentage of short-sided dogs is still quite high. Koren suggested that this was probably due to the positive response that dogs get when they bow their heads.
“Probably something affects the ear or the dogs try to look cute. However, this study is the first step towards finding an answer, and, at least, we now have data to work with,” said Koren in his article. Or perhaps the easiest answer is the best: probably is just a sign of confusion.