Because the Church had always held that the Earth was at the centre of the universe, and it took a long time to gather enough evidence to change this view. Just to say the Sun was at the centre wasn't enough to convince anybody, and it took around 150 more years for the heliocentric theory to gain acceptance after discoveries by Galileo, Kepler and Newton.
Galileo's position was that his discovery of the phases of Venus showed a major flaw in the Ptolemaic theory. This was correct but it did not prove the Copernican theory must be right, because Tycho Brahe came up with an alternative system that explained the phases of Venus while still having the Earth at the centre.
It contradicted the church, which held to the prevailing, centuries-old dominance of Aristotelian science.
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A heliocentric model is a model of the solar system where the Sun is at the center and the planets orbit around it. This is in contrast to the geocentric model, where Earth is considered to be the center of the universe.
In the Heliocentric model, the SUN is in the center. The word 'Helio' refers to SUN. 'Centric' refers to center. So its ' SUN-Center.
Copernicus' heliocentric model provided the framework for Galileo to further explore and confirm through his observations with the telescope. Galileo's discoveries, such as the moons of Jupiter and the phases of Venus, provided empirical evidence in support of the heliocentric model and contributed to its acceptance over the geocentric model.
The current model of the solar system is the "heliocentric system" meaning sun is the center of the solar system. Hope this helps :)