Dogs that have had a lot of strain on the neck due to choke collars can have nerve damage to the pharynx and larynx that could limit their ability to bark. While these issues are often accompanied by breathing issues, not barking is indeed one of the symptoms.
1) Age.
While puppies in general are notorious for barking and/or whining (and isn't it fun when that happens at night?) young puppies have a decreased level of situational awareness.
Much more than adults, they are often lost in the moment and may have trouble focusing. For this same reason, a young Boxer puppy may seem perfectly okay when left home alone, but issues of separation anxiety may develop as he grows older and fully realizes what is happening. From the age of 8 weeks to just about the 5 month mark, it is not all that uncommon for just about nothing to bother a puppy.
At this
age, he may not be aware enough of his extended world to find a reason to bark. If his needs are being met (interaction, plenty of toys, food, water, warmth, comfort) he may not bark at all and this is perfectly normal. In fact, if your Boxer puppy doesn't bark, consider yourself very lucky and do know that this may change very soon.
In regard to age related reasons of not barking, senior Boxers may also be exceedingly quiet. For some older dogs, the triggers that used to cause barking are old news. Those squirrels? Seen them thousands of times, no big deal. The mailman who comes up to the front steps? Well, he's done it about 3000 times and so far he's never actually broken into the house, so no reason to bark anymore; I trust him.
The senior Boxer has heard it all, seen it all and has been exposed to just about every event, situation and element that he is likely to encounter. So, if a senior Boxer doesn't bark, this is usually just a sign that the dog is relaxed, confident with his environment and generally a pretty happy canine family member.
2) No triggers.
While it's highly recommended to expose your Boxer to as many stimuli as possible so that he can learn about the world and all that is in it, in some cases a Boxer may not be introduced to anything that would trigger barking.
If a dog is at home most of the time and is only taken outside for walks in a very quiet neighborhood, he may not bark simply because he has not been presented with a reason to do so. In addition, all needs are being met and the dog is feeling content. It is however, suggested to start bringing the dog to new places and to expose him to other people and other dogs; this is not done to make a Boxer bark but rather is healthy socialization to the world so that he can learn how to react and learn to handle himself well in situations outside of the house and immediate area.
3) Being calm.
What's really cool about dogs is that every one is so unique and even with a particular breed like the Boxer, there's some that are hyped up, some that are super calm and many that are somewhere in-between. There's some that will only bark at really random things like when an owner sings or when seeing just one particular type of person.
In general, barring any
health conditions, if a perfectly healthy Boxer doesn’t bark, this is not a problem at all. It just means that the dog has a calm personality; he's not bothered by things and is displaying easy-going
behavior. While an owner may wish for their Boxer to at least bark at strangers that come up to the house (more on this ahead), you may just want to consider yourself lucky.
4) Rescue dogs.
While behavior can be a bit unpredictable with rescues, many will have inhibited behavior which manifests as being really quiet, not barking, acting shy, timid and even showing signs of anxiety or fear.
We rescued a dog that was about 10 years old and the previous 'owner' claimed the dog was mute. He didn't make a noise for a full 6 months; when he finally did (and it wasn't really quite a bark, it was more like a 'booop' sound), we just about had a heart attack and then celebrated that he found his voice. Even so, he was always a rather quiet dog, never really barking at anything and only making soft noises when he did want to vocalize.