He is the escalator, and we step on it. We may offer our souls and bodies, our sacrifice of praise, and so on, but without Christ they are useless. They are useless unless they are part of his offering. Christ - Christ in all his many ways. This means he offers the bread and wine which is now part of him, and we offer them with him and in him, but only with the result that they are then offered in return to us, and our communion with Christ is consummated in our receiving, eating, drinking.
Offering is remembrance with guts.
It is usually but not always explicitly mentioned in ancient eucharistic prayers, but it is always implicit in the practice and theology of the churches they emanate from. It was never so, for instance, in the immemorial Roman Canon which remained in use up to the Second Vatican Council. Its normal place historically is in the latter part of the prayer, that is, after the Institution narrative, anamnesis and offering. It is there, for instance, in the eucharistic prayers of the Orthodox Divine Liturgy. In the prayers of Common Worship its position varies.