The first paragraph of the speech ends with the phrase “and him only” because the speaker, Red Jacket, is grateful for the beautiful sunny day and for his people’s open eyes and open ears: “for all these favors we thank the Great Spirit, and him only.”
That extra phrase, “and him only,” is significant because it indicates that Red Jacket thanks his god, the Great Spirit, and no other god: not the Christian god that his listeners want him to accept and worship. He refuses. So, the line is significant because it immediately asserts Red Jacket's polite but absolute refusal.
Let’s put these remarks in context. In 1805, Red Jacket, a Seneca orator and chief, also known as Sagoyewatha, delivered some remarks to a Boston missionary society whose members wanted to preach Christianity to the Seneca nation. In these remarks, which some refer to with the title “Red Jacket Defends Native American Religion,” Red Jacket rejects the missionaries’ requests, points out the hypocritical, deceptive, and greedy behavior of the missionaries, and reaffirms the validity of his own religious beliefs.
Let’s take a close look at the whole first paragraph:
Friend and brother; it was the will of the Great Spirit that we should meet together this day. He orders all things, and he has given us a fine day for our council. He has taken his garment from before the sun, and caused it to shine with brightness upon us; our eyes are opened, that we see clearly; our ears are unstopped, that we have been able to hear distinctly the words that you have spoken; for all these favors we thank the Great Spirit, and him only.
Here's what it means. Red Jacket is basically saying,
Look, here we are, meeting together on a beautiful day. We are blessed with healthy bodies; we can see and hear each other and communicate openly. We’re grateful for these favors, and we’re grateful to our god, not yours.