'The Earth's tilt changes through the year'

"The Earth's tilt changes through the year - that's why we have seasons."

The tilt does not change through the year. The Earth's axis is tilted 23.4° and points in a fixed direction - toward Polaris (the North Star) - all year round. The seasons come from the orientation of that fixed tilt relative to the Sun: in June the North Pole leans toward the Sun (summer in the north), in December it leans away (winter). The tilt angle is the same in June and December; only which way it points relative to the Sun changes. (The Earth-Sun distance does vary slightly over the year, but that is not what causes the seasons - it is the tilt's orientation.)

Polaris stays in the same place in the sky all year (the axis points at it); the noon Sun's altitude changes by about 47° (2 × 23.4°) between the solstices while the tilt stays 23.4°; the seasons are opposite in the two hemispheres at the same time (June is summer in the north and winter in the south). A changing tilt would not produce opposite seasons at the same time.