That is not true, sea ice melting does cause sea level increases, you are forgetting that sea water is salt water: https://www.newscientist.com/article/dn18841-melting-iceberg...

"Fresh water, of which icebergs are made, is less dense than salty sea water. So while the amount of sea water displaced by the iceberg is equal to its weight, the melted fresh water will take up a slightly larger volume than the displaced salt water. This results in a small increase in the water level."