English muffins are very similar in texture to various types of bread (gummy and overly soft when fresh) and therefore are better served lightly toasted (as you would for other white or whole grain breads). Bagels are very thick and dense, which actually makes them safer when served untoasted. The reason for this is that untoasted bagels will crumble in your baby’s mouth more easily, and due to how thick and large even half a bagel is, it’s too hard for them to get big pieces in their mouth at once.  It also is harder for those pieces to form one big glob like it would with a strip of soft, thin bread. Baby can suck or munch on the end of a bagel and soften up the ends to get either loose crumbs in their mouth, or get smaller, more manageable pieces that they can chew.  You can also lightly toast a bagel for more resistance, which acts as more of a teether for babies (and less of something they can actually consume). As always, add a nutritious topping or spread to keep it moist and less of a choking risk.