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What Is a Leading Tone? Subtonic vs Leading Tone
The leading tone is the semitone between the 7th scale degree and the tonic note. The leading tone 'points' strongly to the tonic, which is why it's called the leading tone. The subtonic is the whole tone below the tonic, so, with respect to the tonic, the subtonic has much less inherent tension than the leading tone.
So, it’s necessary to provide that Em chord with a leading tone, to make it strongly directional with respect to the Am chord. The way to do this is to sharpen the G in the Em chord, converting it into an E major chord.
When you do that, and progress from E major to A minor, you move from these notes:
E – G♯ – B
to these notes:
A – C – E
Now the relationship of the note G♯ in the E major chord (the chord being left behind) with respect to the root note A (the foundation note) in the new chord, A minor, is 7 – 1 (8), a semitone.