"....why does turbo tax show the trust paying the capital gains tax?"
Consistent with Treas. Reg. §1.643(a)-3(a), the default mode for TurboTax is to treat capital gains as part of the trust corpus which remains with the trust and is not available for distribution to the beneficiary(ies).
However, circumstances delineated in Treas. Reg. §1.643(a)-3(b) (reproduced below) provide for the distribution of capital gains to the beneficiary(ies). If that Reg section is applicable, you can easily change the default distribution scheme in TurboTax by allocating capital gains to the beneficiary(ies). [see screenshot]
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§1.643(a)-3:
(b)
Capital gains included in distributable net income.
Gains from the sale or exchange of
capital assets are included in distributable net income to the extent
they are, pursuant to the terms of the governing instrument and
applicable local law, or pursuant to a reasonable and impartial exercise
of discretion by the fiduciary (in accordance with a power granted to
the fiduciary by applicable local law or by the governing instrument if
not prohibited by applicable local law)—
(1)
Allocated to income (but if income
under the state statute is defined as, or consists of, a unitrust
amount, a discretionary power to allocate gains to income must also be
exercised consistently and the amount so allocated may not be greater
than the excess of the unitrust amount over the amount of distributable
net income determined without regard to this subparagraph §1.643(a)-3(b));
(2)
Allocated to corpus but treated
consistently by the fiduciary on the trust's books, records, and tax
returns as part of a distribution to a beneficiary; or
(3)
Allocated to corpus but actually
distributed to the beneficiary or utilized by the fiduciary in
determining the amount that is distributed or required to be distributed
to a beneficiary.
