A dog who likes food indoors may ignore it on a busy street. That does not prove stubbornness. The outside world may be more interesting than the treat; stress can also make a dog less responsive. First check the setting, your dog's body language, and whether they normally eat.
Make the exercise easier
Move farther from the distraction or return to a quiet place. If the dog is worried, frozen, or barking, leave the situation rather than trying to lure them closer with food. If they are relaxed but interested in smells instead, practice with smaller distractions and try rewards your dog actually values: a favorite food, a toy, or permission to sniff safely. Use food that agrees with their diet and health needs.
Where should I start?
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Follow your dog, not a treat ladder
There is no universal rule that kibble works only at home or chicken works outdoors. Each dog and each day is different. Reward easy successes and build up distractions gradually. If your dog abruptly loses appetite in ordinary settings, seems ill, or will not eat as usual, contact your veterinarian.