Why 'não acho que' takes the subjunctive
Portuguese verbs of opinion such as achar, pensar and crer are followed by the indicative when you state what you think: acho que é. As soon as you put não in front of them, the verb in the que clause usually switches to the subjunctive: não acho que seja. The opinion verb stays the same, but the verb after it changes mood.
English speakers often miss this because English has no such change. I think he is and I don't think he is use exactly the same form of to be. So learners add não and forget to change the second verb. The result, não acho que é, sounds off to many native ears.
The logic is about commitment. An affirmative opinion presents the idea as something you hold to be true, so Portuguese uses the indicative, the mood of facts. A negated opinion presents the idea as doubtful or unreal, so Portuguese uses the subjunctive, the mood of uncertainty.
Rule of thumb: opinion verb + que takes the indicative, and não + opinion verb + que takes the subjunctive. Only the verb in the que clause changes.
In the first half, está is indicative. In the second half, the negation turns it into esteja, the present subjunctive of estar.
achar, pensar and crer all mean to think or to believe in the sense of holding an opinion. achar is the most common in everyday speech. pensar is a little more reflective, and crer sounds more formal or written.
acreditar means to believe, as in to accept something as true. It follows the same switch, and não acredito que is also a very common way to express surprise or disbelief.
supor and imaginar express a guess or assumption. They also take the indicative when affirmative and the subjunctive when negated.
parecer works the same way in the impersonal pattern parece que, meaning it seems that.
The typical mistake is keeping the indicative after the negation: não acho que ele está sozinho instead of não acho que ele esteja sozinho. When you say não before an opinion verb, check the verb after que.
The switch is a strong tendency, not an automatic rule. In relaxed speech, especially in Brazil, you will hear the indicative after a negated opinion verb when the speaker feels fairly sure. Using the subjunctive is always the safe choice for learners.
With supor and imaginar, speakers sometimes use the subjunctive even in the affirmative to sound more tentative, as in suponho que seja isso. That is fine, but the negated form still leans firmly towards the subjunctive.
Do not confuse these verbs with duvidar and negar. Those two express doubt or denial on their own, so they take the subjunctive even without não.
After achar, pensar, crer, acreditar, supor, imaginar and parece que, use the indicative when you state an opinion. Add não and switch the verb after que to the subjunctive: acho que é becomes não acho que seja.