Stating Beliefs
When you express what you believe or think is true, you are declaring a fact from your perspective. Because you are stating your reality, verbs like creer (to believe) and pensar (to think) followed by que take the indicative mood.
| I believe the politician exaggerates in the debate. | Creo que el político exagera en el debate. |
| I think your opinion is interesting. | Pienso que tu opinión es interesante. |
Expressing Skepticism
However, when you add no in front of these verbs, everything changes. Saying that you don't believe or don't think something introduces doubt and skepticism. Because you are questioning whether a claim is true, no creer que and no pensar que trigger the subjunctive mood.
| I don't believe the argument convinces the politician. | No creo que el argumento convenza al político. |
| We don't think the evidence is true. | No pensamos que la evidencia sea verdadera. |
A Direct Comparison
Notice how simply adding no to the beginning of the sentence shifts the second verb from declaring a fact (indicative) to expressing doubt (subjunctive):
| I believe the conclusion of the debate is clear. | Creo que la conclusión del debate es clara. |
| I don't believe the conclusion is logical. | No creo que la conclusión sea lógica. |
When asking a question with affirmative verbs of belief, you generally stick to the indicative, since you are simply asking the other person to state their reality:
| Do you believe the argument is valid? | ¿Crees que el argumento es válido? |