shell script, loop array, why use ${array[@]}

This is the syntax defined by the language. This is just how it works. Read about it in man bash, search for the section titled "Arrays". Here's the relevant part:

Any element of an array may be referenced using ${name[subscript]}. The braces are required to avoid conflicts with pathname expansion. If subscript is @ or * , the word expands to all members of name. These subscripts differ only when the word appears within double quotes. If the word is double-quoted, ${name[*]} expands to a single word with the value of each array member separated by the first character of the IFS special variable, and ${name[@]} expands each element of name to a sep‐ arate word. When there are no array members, ${name[@]} expands to nothing. If the double-quoted expansion occurs within a word, the expansion of the first parameter is joined with the beginning part of the original word, and the expansion of the last parameter is joined with the last part of the original word. This is analogous to the expansion of the special parameters * and @ (see Special Parameters above).