It would be better to have a light snack, like a piece of fruit or small bowl of granola, than to force yourself to eat a full meal if you are not hungry.
Do eat something, just eat small until you train your body to accept food in the morning.
There are a few possible scenarios for why I'd think someone wouldn't eat breakfast. Since you didn't specify your situation, I'm including a few.
Now let's say you do tend to be absolutely starving at lunchtime, maybe even hungry for a couple hours before (this is assuming you get up early in the morning, before 8). Then you may want to consider bringing a breakfast with you to eat at, let's say, 9. If you have a long transfer to work, maybe by train and you get up far too early (like around 5) to be hungry, but you get hungry later on, then I'd recommend bringing something you can eat during transfer, or immediately when you get to work/school (if you drive a car all the way to work you can't exactly eat while doing so).
Let's say you get up at 10-11 and are going to have lunch at 12-13. Then you can definitely skip breakfast altogether, if you wake up and are not especially hungry.
This all depends on your personal health and circadian rhythm (biological clock, has your daily sleeping + eating 'schedule'). Please note that if your doctor has told you you need to have breakfast in the morning, due to some medical reason, then that advice should be taken before mine.
Suggestions on breakfast items to bring with you: sandwiches; yoghurt and granola in one of those reusable cups for this purpose; fruit salad; smoothie. You can of course buy some of these items in stores, in single portions, but it's usually best to make your own, both nutritionally and economically.
I hope my very long answer helped you out somehow and good luck figuring out what works best for you!
If you don’t feel hungry even after drinking water then don’t force yourself but be ready to get hungry 1-2 hours later so you should take healthy snacks with you
I used to skip breakfast everyday for most of my life. I know the temptation to keep it up.
I started having something simple in the mornings, toast with butter, toast with jam, toast with peanut butter. I love coffee, of course have your coffee.
Upgrade after a while, when your ready, plain Greek yogurt with berries or banana, add granola or a handful of nuts.
Try cottage cheese with fruit, granola and/or nuts.
Upgrade again after a while, try a quiche.
You'll feel more energized for the day, you'll be more focused with fuel in your body to feed your brain and fuel your body for the day.