As previously stated, it would be too broken if you could activate it during your own battle phase. Look at it like this:
Say you have "Berzerk Gorilla" on your side of the field, and your opponent only has "Gemini Elf". The cards in your hand are "Spirit Reaper", "End of Anubis" and "Blue Eyes White Dragon". If you could activate "Ultimate Offering" during your battle phase you can:
1) Attack with "Berzerk Gorilla", destroying "Gemini Elf" (inflict 100 damage)
2) Summon "Spirit Reaper" and attack (inflict 300 and force a discard).
3) Offer "Spirit Reaper" as a tribute and summon "End of Anubis" and attack (inflict 2500)
4) Offer the rest as a tribute again and summon BEWD (inflict 3000)
So for a small price to pay, you've just inflicted 5900 damage, and forced a discard.
Without that restriction, your options are far more limited and you need to decide what would be best for the situation.
- Andrew