This seems to be "just a rule", there's some discussion of it at this questionat this question.
Some surrounding thoughts to think about though. Non-stative verbs in the plain form are interpreted as talking about the future, unless the action is generic or habitual. ジョンが食べる
means either "John will eat", or "John eats(habitually/regularly)". To talk about an activity that continues, you switch to the stative form ~ている. (See Derek's excellent coverage herehere)
In the case of 言う or 思う, the non-past seems to have an implication of "I (typically) say" or "I (tend to) think". Moving that to the stative seems to pick up an implication of "I (obstinately) say ...", or "I'm (stuck) thinking...". It seems to be polite to emphasize the ephemeral nature of your own statements or thoughts.
Confusingly, the structure that implies boorishness in oneself is seen as a virtue of consistency in someone else.