If "I'm thinking" is correct, why isn't "I'm knowing" correct in formal English?
think+ing = thinking is correct
know+ing = knowing isn't correct
Verbs can be considered to be either action verbs or state verbs. Action verbs, are the verbs used to convey an action, eg run, jump, dance, fight, etc. State verbs, however, usually do not convey an action but they convey information about our ideas, thoughts, feelings and existence, eg think, feel (as in emotion, not as in touching), know, believe, be or have.
State verbs are rarely used in the continuous tense. Action verbs are often used in this tense. This is because the continuous indicates that something is happening now (although it may have commenced in the past), and will probably cease at some stage in the future. So, it contains an implied message that whatever is being done is temporary. This is reasonable for action verbs; in the absence of perpetual motion, we expect most actions to cease at some stage.
A state, as opposed to an action, has a more permanent character associated with it, eg if you know something then, assuming what you know is correct, it is not likely that you will suddenly cease knowing. (Please note that "knowing" at the end of the previous sentence is a participle, not the continuous form of the verb to know.)
So, whereas a native English speaker will say 'I am riding my bike', or 'I am going into town', it is unlikely that they would say 'I am knowing Mr Smith', or 'I am loving my house'. They would more likely say, 'I know Mr Smith, or 'I love my house'.
There are exceptions to what I have said about state verbs, but it usually involves state verbs when they are used to describe non-permanent states. e.g. You should not say,"I am having a car", but you could say,"I have a car". However, it it is acceptable to say, 'I am having a good time', because that is a only temporary state. Similarly you might say, 'I am being quiet', but not 'I am being alive'.