You may be inadvertently encouraging clingy behavior.
Your Chihuahua is highly aware of all your emotions, the tone in which you speak to him, and even your body language. You can't really hide anything from a dog, and how you act sends out a vibe.
If your overall vibes says 'Oh, you poor little thing, let me cuddle you right up and take care of my little baby!', you can guess that this won't help a Chihuahua be more independent.
But, maybe your actions and words are not quite so literal. Even so, it can have the same effect.
When you get home, do you rush over to your Chihuahua? While it is human instinct to do so, it can actually send the wrong message to a dog and cause him to become clingier than ever. When dogs are home without their owners, they are metaphorically thinking, "Will she ever come back?' and 'What if I never see him again?'.