How does metta sutra develop loving kindness Metta sutra says "May all living beings be happy minded." This seems illogical to me as all living beings cannot be happy minded at a particular moment of time. I also feel that contemplating on anything that is false will not lead me to the ultimate truth. In my view loving kindness should be better cultivated by knowing the true nature of things because if we get insight into real nature of things then we will automatically develop kindness by clearly seeing dukkha and we would be able to understand the suffering of others in a better way. Note: I do not intend to offend great Buddhist scriptures. I asked this question to clear my ignorance.
When you understand the suffering of others, this would result in you developing your compassion (karuna) and not exactly loving kindness (metta). So, compassion is a bit different. Compassion is how one deals with others' suffering (dukkha) while renunciation is how one deals with one's own suffering. Of course, there may be some overlap between the two.

Then what about loving kindness (metta)? This term metta has also been translated as benevolence, friendliness, amity, good will and universal love.

You're perfectly right that all beings cannot be happy-minded at once.

Cultivating metta is about changing YOUR state of mind, and not actually changing other people's state of mind.

Loving kindness is about you changing your thoughts, emotions, intentions, attitude, outlook and conduct, in such a way that it radiates with benevolence and friendliness to all beings (including yourself). It is so that you become the true friend who wishes everyone, without discrimination, to be happy and at ease with themselves. Loving kindness is a cure for one's ill will towards others.

On the other hand, compassion is about you trying to understand the suffering of others and trying to alleviate the suffering of others, or at least not make it worse. Compassion is a cure for one's contempt for others.