In DQN, why not use target network to predict current state Q values?
Bellman equation for deterministic environments is given as follows
$$
V(s) = max_aR(s, a) + \gamma V(s')
$$
Where $V$ is a value function, $R$ is a reward function, $s$ is current state, $s'$ is next state, $a$ is an action. In DQN when optimizing $V$ it is assumed that $V(s')$ has on average lower error than $V(s)$. This is intuitively because $s'$ is closer to the end state for which $V$ is known and so there are fewer steps in which error can accumulate. This way we can progressively lower errors of $V$ for all states starting from the end states up to the starting state. I don't know how exactly you use current state to update weights but assuming it looks like this
$$
\delta V(s) := \alpha(max_aR(s, a) + \gamma V(s) - V(s))
$$
instead of
$$
\delta V(s) := \alpha(max_aR(s, a) + \gamma V(s') - V(s))
$$
i.e. you don't use $V(s')$ in the weights update what happens is the same error propagates over and over again because information about rewards in the later states is not propagated to earlier states.
As a concrete example imagine an environment with 3 states $s_1$, $s_2$ and $s_3$ where $s_1$ is starting state $s_3$ is the end state, the action space is only one move: go from state $s_i$ to state $s_{i+1}$ and reward function is 1 for moving to $s_3$ and 0 otherwise. What happens then is
$$
\delta V(s_3) = 0 \\
\delta V(s_2) = \alpha (max_a(R(s_2, a) + \gamma V(s_2) - V(s_2)) = \alpha (1 + \gamma V(s_2) - V(s_2)) \\
\delta V(s_1) = \alpha (max_a(R(s_1, a) + \gamma V(s_1) - V(s_1)) = \alpha (0 + \gamma V(s_1) - V(s_1))
$$
Because starting value for $V(s_1)$ is 0 it's gradient will always be 0 and the network will never learn the value of this state. That's why it must take a loook at values of its next state.